Actuarial Science

  1. Mathematical and Statistical Foundations
    1. Probability Theory
      1. Fundamental Concepts
        1. Sample Spaces and Events
          1. Definition of Sample Space
            1. Types of Events
              1. Event Operations
                1. Sigma-Algebras
                2. Axioms of Probability
                  1. Kolmogorov Axioms
                    1. Properties Derived from Axioms
                      1. Probability Measures
                        1. Finite and Countable Spaces
                        2. Set Theory in Probability
                          1. Union and Intersection
                            1. Complement Operations
                              1. De Morgan's Laws
                                1. Venn Diagrams
                                2. Probability Rules
                                  1. Addition Rule
                                    1. Multiplication Rule
                                      1. Complement Rule
                                        1. Inclusion-Exclusion Principle
                                      2. Combinatorial Principles
                                        1. Counting Principles
                                          1. Fundamental Counting Principle
                                            1. Addition Principle
                                              1. Multiplication Principle
                                                1. Pigeonhole Principle
                                                2. Permutations
                                                  1. Permutations without Repetition
                                                    1. Permutations with Repetition
                                                      1. Circular Permutations
                                                        1. Restricted Permutations
                                                        2. Combinations
                                                          1. Combinations without Repetition
                                                            1. Combinations with Repetition
                                                              1. Pascal's Triangle
                                                                1. Binomial Coefficients
                                                                2. Multinomial Coefficients
                                                                  1. Definition and Properties
                                                                    1. Relationship to Binomial Coefficients
                                                                      1. Computational Methods
                                                                    2. Conditional Probability and Independence
                                                                      1. Conditional Probability
                                                                        1. Definition and Interpretation
                                                                          1. Properties of Conditional Probability
                                                                            1. Conditional Probability as Probability Measure
                                                                              1. Geometric Interpretation
                                                                              2. Multiplication Rule
                                                                                1. General Multiplication Rule
                                                                                  1. Chain Rule
                                                                                    1. Tree Diagrams
                                                                                    2. Law of Total Probability
                                                                                      1. Partition of Sample Space
                                                                                        1. Formula and Applications
                                                                                          1. Continuous Version
                                                                                            1. Multiple Partitions
                                                                                            2. Bayes' Theorem
                                                                                              1. Statement and Proof
                                                                                                1. Prior and Posterior Probabilities
                                                                                                  1. Applications in Actuarial Science
                                                                                                    1. Bayesian Updating
                                                                                                    2. Independence of Events
                                                                                                      1. Definition of Independence
                                                                                                        1. Mutual Independence
                                                                                                          1. Pairwise Independence
                                                                                                            1. Conditional Independence
                                                                                                          2. Random Variables
                                                                                                            1. Discrete Random Variables
                                                                                                              1. Definition and Examples
                                                                                                                1. Range and Support
                                                                                                                  1. Probability Mass Function
                                                                                                                    1. Properties and Characteristics
                                                                                                                    2. Continuous Random Variables
                                                                                                                      1. Definition and Examples
                                                                                                                        1. Probability Density Function
                                                                                                                          1. Relationship to Cumulative Distribution Function
                                                                                                                            1. Properties and Characteristics
                                                                                                                            2. Mixed Random Variables
                                                                                                                              1. Definition and Examples
                                                                                                                                1. Probability Function
                                                                                                                                  1. Special Cases
                                                                                                                                  2. Indicator Variables
                                                                                                                                    1. Definition and Properties
                                                                                                                                      1. Applications in Probability
                                                                                                                                        1. Expectation and Variance
                                                                                                                                          1. Combinations of Indicators
                                                                                                                                        2. Probability Distributions
                                                                                                                                          1. Probability Mass Function
                                                                                                                                            1. Definition and Properties
                                                                                                                                              1. Normalization Condition
                                                                                                                                                1. Relationship to CDF
                                                                                                                                                  1. Examples and Applications
                                                                                                                                                  2. Probability Density Function
                                                                                                                                                    1. Definition and Properties
                                                                                                                                                      1. Normalization Condition
                                                                                                                                                        1. Relationship to CDF
                                                                                                                                                          1. Examples and Applications
                                                                                                                                                          2. Cumulative Distribution Function
                                                                                                                                                            1. Definition and Properties
                                                                                                                                                              1. Right Continuity
                                                                                                                                                                1. Inverse Function
                                                                                                                                                                  1. Empirical Distribution Function
                                                                                                                                                                  2. Quantile Function
                                                                                                                                                                    1. Definition and Properties
                                                                                                                                                                      1. Percentiles and Quartiles
                                                                                                                                                                        1. Inverse CDF
                                                                                                                                                                          1. Applications in Risk Management
                                                                                                                                                                        2. Expectation and Moments
                                                                                                                                                                          1. Expected Value
                                                                                                                                                                            1. Definition for Discrete Variables
                                                                                                                                                                              1. Definition for Continuous Variables
                                                                                                                                                                                1. Properties of Expectation
                                                                                                                                                                                  1. Linearity of Expectation
                                                                                                                                                                                  2. Variance and Standard Deviation
                                                                                                                                                                                    1. Definition and Calculation
                                                                                                                                                                                      1. Properties of Variance
                                                                                                                                                                                        1. Computational Formulas
                                                                                                                                                                                          1. Coefficient of Variation
                                                                                                                                                                                          2. Covariance and Correlation
                                                                                                                                                                                            1. Definition of Covariance
                                                                                                                                                                                              1. Properties of Covariance
                                                                                                                                                                                                1. Correlation Coefficient
                                                                                                                                                                                                  1. Linear Relationships
                                                                                                                                                                                                  2. Higher-Order Moments
                                                                                                                                                                                                    1. Raw Moments
                                                                                                                                                                                                      1. Central Moments
                                                                                                                                                                                                        1. Standardized Moments
                                                                                                                                                                                                          1. Moment Relationships
                                                                                                                                                                                                          2. Skewness and Kurtosis
                                                                                                                                                                                                            1. Measures of Asymmetry
                                                                                                                                                                                                              1. Measures of Tail Behavior
                                                                                                                                                                                                                1. Interpretation and Applications
                                                                                                                                                                                                                  1. Sample Estimates
                                                                                                                                                                                                                  2. Moment Generating Functions
                                                                                                                                                                                                                    1. Definition and Properties
                                                                                                                                                                                                                      1. Uniqueness Theorem
                                                                                                                                                                                                                        1. Applications to Distribution Theory
                                                                                                                                                                                                                          1. Cumulant Generating Functions
                                                                                                                                                                                                                          2. Properties of Expectation
                                                                                                                                                                                                                            1. Expectation of Functions
                                                                                                                                                                                                                              1. Jensen's Inequality
                                                                                                                                                                                                                                1. Conditional Expectation
                                                                                                                                                                                                                                  1. Law of Total Expectation
                                                                                                                                                                                                                                2. Common Probability Distributions
                                                                                                                                                                                                                                  1. Discrete Distributions
                                                                                                                                                                                                                                    1. Bernoulli Distribution
                                                                                                                                                                                                                                      1. Definition and Parameters
                                                                                                                                                                                                                                        1. Moments and Properties
                                                                                                                                                                                                                                          1. Relationship to Other Distributions
                                                                                                                                                                                                                                          2. Binomial Distribution
                                                                                                                                                                                                                                            1. Definition and Parameters
                                                                                                                                                                                                                                              1. Moments and Properties
                                                                                                                                                                                                                                                1. Normal Approximation
                                                                                                                                                                                                                                                  1. Applications in Insurance
                                                                                                                                                                                                                                                  2. Poisson Distribution
                                                                                                                                                                                                                                                    1. Definition and Parameters
                                                                                                                                                                                                                                                      1. Moments and Properties
                                                                                                                                                                                                                                                        1. Poisson Process
                                                                                                                                                                                                                                                          1. Applications in Claim Modeling
                                                                                                                                                                                                                                                          2. Geometric Distribution
                                                                                                                                                                                                                                                            1. Definition and Parameters
                                                                                                                                                                                                                                                              1. Memoryless Property
                                                                                                                                                                                                                                                                1. Moments and Properties
                                                                                                                                                                                                                                                                2. Negative Binomial Distribution
                                                                                                                                                                                                                                                                  1. Definition and Parameters
                                                                                                                                                                                                                                                                    1. Relationship to Geometric
                                                                                                                                                                                                                                                                      1. Moments and Properties
                                                                                                                                                                                                                                                                        1. Applications in Frequency Modeling
                                                                                                                                                                                                                                                                        2. Hypergeometric Distribution
                                                                                                                                                                                                                                                                          1. Definition and Parameters
                                                                                                                                                                                                                                                                            1. Sampling without Replacement
                                                                                                                                                                                                                                                                              1. Moments and Properties
                                                                                                                                                                                                                                                                              2. Multinomial Distribution
                                                                                                                                                                                                                                                                                1. Definition and Parameters
                                                                                                                                                                                                                                                                                  1. Relationship to Binomial
                                                                                                                                                                                                                                                                                2. Continuous Distributions
                                                                                                                                                                                                                                                                                  1. Uniform Distribution
                                                                                                                                                                                                                                                                                    1. Definition and Parameters
                                                                                                                                                                                                                                                                                      1. Moments and Properties
                                                                                                                                                                                                                                                                                        1. Random Number Generation
                                                                                                                                                                                                                                                                                        2. Normal Distribution
                                                                                                                                                                                                                                                                                          1. Definition and Parameters
                                                                                                                                                                                                                                                                                            1. Standard Normal Distribution
                                                                                                                                                                                                                                                                                              1. Properties and Characteristics
                                                                                                                                                                                                                                                                                                1. Central Limit Theorem Applications
                                                                                                                                                                                                                                                                                                2. Exponential Distribution
                                                                                                                                                                                                                                                                                                  1. Definition and Parameters
                                                                                                                                                                                                                                                                                                    1. Memoryless Property
                                                                                                                                                                                                                                                                                                      1. Relationship to Poisson Process
                                                                                                                                                                                                                                                                                                        1. Applications in Survival Analysis
                                                                                                                                                                                                                                                                                                        2. Gamma Distribution
                                                                                                                                                                                                                                                                                                          1. Definition and Parameters
                                                                                                                                                                                                                                                                                                            1. Special Cases
                                                                                                                                                                                                                                                                                                              1. Moments and Properties
                                                                                                                                                                                                                                                                                                                1. Applications in Loss Modeling
                                                                                                                                                                                                                                                                                                                2. Beta Distribution
                                                                                                                                                                                                                                                                                                                  1. Definition and Parameters
                                                                                                                                                                                                                                                                                                                    1. Moments and Properties
                                                                                                                                                                                                                                                                                                                      1. Applications in Bayesian Analysis
                                                                                                                                                                                                                                                                                                                        1. Relationship to Other Distributions
                                                                                                                                                                                                                                                                                                                        2. Lognormal Distribution
                                                                                                                                                                                                                                                                                                                          1. Definition and Parameters
                                                                                                                                                                                                                                                                                                                            1. Relationship to Normal Distribution
                                                                                                                                                                                                                                                                                                                              1. Moments and Properties
                                                                                                                                                                                                                                                                                                                                1. Applications in Financial Modeling
                                                                                                                                                                                                                                                                                                                                2. Pareto Distribution
                                                                                                                                                                                                                                                                                                                                  1. Definition and Parameters
                                                                                                                                                                                                                                                                                                                                    1. Heavy-Tailed Properties
                                                                                                                                                                                                                                                                                                                                      1. Moments and Properties
                                                                                                                                                                                                                                                                                                                                        1. Applications in Loss Modeling
                                                                                                                                                                                                                                                                                                                                        2. Weibull Distribution
                                                                                                                                                                                                                                                                                                                                          1. Definition and Parameters
                                                                                                                                                                                                                                                                                                                                            1. Hazard Function
                                                                                                                                                                                                                                                                                                                                              1. Moments and Properties
                                                                                                                                                                                                                                                                                                                                                1. Applications in Reliability
                                                                                                                                                                                                                                                                                                                                            2. Joint, Marginal, and Conditional Distributions
                                                                                                                                                                                                                                                                                                                                              1. Joint Distributions
                                                                                                                                                                                                                                                                                                                                                1. Joint Probability Mass Function
                                                                                                                                                                                                                                                                                                                                                  1. Joint Probability Density Function
                                                                                                                                                                                                                                                                                                                                                    1. Joint Cumulative Distribution Function
                                                                                                                                                                                                                                                                                                                                                      1. Properties and Relationships
                                                                                                                                                                                                                                                                                                                                                      2. Marginal Distributions
                                                                                                                                                                                                                                                                                                                                                        1. Marginal PMF and PDF
                                                                                                                                                                                                                                                                                                                                                          1. Calculation Methods
                                                                                                                                                                                                                                                                                                                                                            1. Relationship to Joint Distribution
                                                                                                                                                                                                                                                                                                                                                            2. Conditional Distributions
                                                                                                                                                                                                                                                                                                                                                              1. Conditional PMF and PDF
                                                                                                                                                                                                                                                                                                                                                                1. Conditional Expectation
                                                                                                                                                                                                                                                                                                                                                                2. Independence of Random Variables
                                                                                                                                                                                                                                                                                                                                                                  1. Definition and Tests
                                                                                                                                                                                                                                                                                                                                                                    1. Properties of Independent Variables
                                                                                                                                                                                                                                                                                                                                                                      1. Sums of Independent Variables
                                                                                                                                                                                                                                                                                                                                                                        1. Products of Independent Variables
                                                                                                                                                                                                                                                                                                                                                                        2. Covariance and Correlation of Random Variables
                                                                                                                                                                                                                                                                                                                                                                          1. Calculation Methods
                                                                                                                                                                                                                                                                                                                                                                            1. Interpretation
                                                                                                                                                                                                                                                                                                                                                                              1. Portfolio Applications
                                                                                                                                                                                                                                                                                                                                                                            2. Functions of Random Variables
                                                                                                                                                                                                                                                                                                                                                                              1. Distribution of Functions of Random Variables
                                                                                                                                                                                                                                                                                                                                                                                1. Transformation Method
                                                                                                                                                                                                                                                                                                                                                                                  1. CDF Method
                                                                                                                                                                                                                                                                                                                                                                                    1. Moment Generating Function Method
                                                                                                                                                                                                                                                                                                                                                                                      1. Delta Method
                                                                                                                                                                                                                                                                                                                                                                                      2. Change of Variables Technique
                                                                                                                                                                                                                                                                                                                                                                                        1. One-to-One Transformations
                                                                                                                                                                                                                                                                                                                                                                                          1. Many-to-One Transformations
                                                                                                                                                                                                                                                                                                                                                                                            1. Jacobian Method
                                                                                                                                                                                                                                                                                                                                                                                            2. Convolution
                                                                                                                                                                                                                                                                                                                                                                                              1. Definition and Properties
                                                                                                                                                                                                                                                                                                                                                                                                1. Discrete Convolution
                                                                                                                                                                                                                                                                                                                                                                                                  1. Continuous Convolution
                                                                                                                                                                                                                                                                                                                                                                                                    1. Applications to Sums
                                                                                                                                                                                                                                                                                                                                                                                                  2. Limit Theorems
                                                                                                                                                                                                                                                                                                                                                                                                    1. Law of Large Numbers
                                                                                                                                                                                                                                                                                                                                                                                                      1. Weak Law of Large Numbers
                                                                                                                                                                                                                                                                                                                                                                                                        1. Statement and Conditions
                                                                                                                                                                                                                                                                                                                                                                                                          1. Proof Outline
                                                                                                                                                                                                                                                                                                                                                                                                            1. Convergence in Probability
                                                                                                                                                                                                                                                                                                                                                                                                            2. Strong Law of Large Numbers
                                                                                                                                                                                                                                                                                                                                                                                                              1. Statement and Conditions
                                                                                                                                                                                                                                                                                                                                                                                                                1. Almost Sure Convergence
                                                                                                                                                                                                                                                                                                                                                                                                                  1. Relationship to Weak Law
                                                                                                                                                                                                                                                                                                                                                                                                                2. Central Limit Theorem
                                                                                                                                                                                                                                                                                                                                                                                                                  1. Classical Central Limit Theorem
                                                                                                                                                                                                                                                                                                                                                                                                                    1. Lindeberg-Lévy Theorem
                                                                                                                                                                                                                                                                                                                                                                                                                      1. Lyapunov Theorem
                                                                                                                                                                                                                                                                                                                                                                                                                        1. Berry-Esseen Theorem
                                                                                                                                                                                                                                                                                                                                                                                                                        2. Applications in Actuarial Science
                                                                                                                                                                                                                                                                                                                                                                                                                          1. Risk Pooling
                                                                                                                                                                                                                                                                                                                                                                                                                            1. Premium Calculation
                                                                                                                                                                                                                                                                                                                                                                                                                              1. Solvency Assessment
                                                                                                                                                                                                                                                                                                                                                                                                                                1. Simulation Studies
                                                                                                                                                                                                                                                                                                                                                                                                                            2. Statistics and Data Analysis
                                                                                                                                                                                                                                                                                                                                                                                                                              1. Descriptive Statistics
                                                                                                                                                                                                                                                                                                                                                                                                                                1. Measures of Central Tendency
                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Mean
                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Median
                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Mode
                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Trimmed Mean
                                                                                                                                                                                                                                                                                                                                                                                                                                        2. Measures of Variability
                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Range
                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Variance
                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Standard Deviation
                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Interquartile Range
                                                                                                                                                                                                                                                                                                                                                                                                                                                2. Measures of Shape
                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Skewness
                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Kurtosis
                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Box Plots
                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Histograms
                                                                                                                                                                                                                                                                                                                                                                                                                                                        2. Data Visualization
                                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Scatter Plots
                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Time Series Plots
                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Probability Plots
                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Quantile-Quantile Plots
                                                                                                                                                                                                                                                                                                                                                                                                                                                              2. Statistical Inference
                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Point Estimation
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Method of Moments
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Maximum Likelihood Estimation
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Properties of Estimators
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Bias and Efficiency
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        2. Interval Estimation
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Confidence Intervals
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Bootstrap Methods
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Bayesian Credible Intervals
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Prediction Intervals
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                2. Hypothesis Testing
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Null and Alternative Hypotheses
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Type I and Type II Errors
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Test Statistics
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. P-values and Critical Values
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        2. Goodness of Fit Tests
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Chi-Square Test
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Kolmogorov-Smirnov Test
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Anderson-Darling Test
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Likelihood Ratio Tests
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              2. Regression Analysis
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Simple Linear Regression
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Model Assumptions
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Parameter Estimation
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Inference for Parameters
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Model Diagnostics
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        2. Multiple Linear Regression
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Model Specification
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Parameter Estimation
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Model Selection
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Multicollinearity
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                2. Generalized Linear Models
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Exponential Family
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Parameter Estimation
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Model Diagnostics
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      2. Time Series Analysis
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Trend and Seasonality
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Autoregressive Models
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Moving Average Models
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. ARIMA Models
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          2. Financial Mathematics
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Theory of Interest
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Time Value of Money
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Present Value Concept
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Future Value Concept
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Equivalence of Cash Flows
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Real vs. Nominal Interest Rates
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      2. Interest Rate Measurement
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Simple Interest
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Definition and Formula
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Limitations
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Comparison with Compound Interest
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              2. Compound Interest
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Definition and Formula
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Frequency of Compounding
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Continuous Compounding
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    2. Nominal vs. Effective Rates
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Nominal Interest Rate
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Effective Annual Rate
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Conversion Formulas
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          2. Force of Interest
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Definition and Properties
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Relationship to Other Interest Measures
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Continuous Compounding
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              2. Discounting and Accumulation
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Present Value Factors
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Accumulation Factors
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Discount Factors
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Relationship Between Factors
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      2. Present and Accumulated Value Factors
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Single Payment Factors
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Series Payment Factors
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Perpetuity Factors
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Applications in Valuation
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            2. Annuities
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Annuity-Immediate and Annuity-Due
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Definitions and Notation
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Present Value Calculations
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Accumulated Value Calculations
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Relationship Between Types
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      2. Level Payment Annuities
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Ordinary Annuities
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Annuities Due
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Deferred Annuities
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Perpetuities
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              2. Varying Annuities
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Arithmetically Increasing Annuities
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Present Value Formulas
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Accumulated Value Formulas
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Special Cases
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      2. Arithmetically Decreasing Annuities
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Present Value Formulas
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Accumulated Value Formulas
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Special Cases
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            2. Geometrically Increasing Annuities
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Present Value Formulas
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Accumulated Value Formulas
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Inflation Adjustments
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  2. Geometrically Decreasing Annuities
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Present Value Formulas
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Accumulated Value Formulas
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Special Cases
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      2. Continuous Annuities
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Continuous Payment Streams
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Present Value Calculations
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Accumulated Value Calculations
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            2. Perpetuities
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Level Perpetuities
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Increasing Perpetuities
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Decreasing Perpetuities
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  2. Deferred Annuities
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Deferred Ordinary Annuities
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Deferred Annuities Due
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Present Value Calculations
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      2. Loans and Amortization
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Loan Structure and Terms
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Principal Amount
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Interest Rate
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Repayment Period
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Payment Frequency
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                2. Amortization Method
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Level Payment Loans
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Interest and Principal Components
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Amortization Schedules
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Outstanding Balance Calculations
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        2. Sinking Fund Method
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Sinking Fund Concept
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Payment Calculations
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Fund Accumulation
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Comparison with Amortization
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                2. Loan Schedules
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Payment Schedules
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Interest Schedules
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Principal Schedules
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Balance Schedules
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        2. Outstanding Loan Balance
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Prospective Method
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Retrospective Method
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Refinancing Considerations
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            2. Bonds and Other Securities
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Bond Pricing
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Present Value of Cash Flows
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Coupon Payments
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Principal Repayment
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Market Price Determination
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      2. Yield to Maturity
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Definition and Calculation
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Relationship to Bond Price
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Yield Curves
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            2. Duration and Convexity
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Macaulay Duration
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Modified Duration
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Effective Duration
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Convexity Measures
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    2. Callable and Putable Bonds
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Call Options
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Put Options
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Option-Adjusted Spreads
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Valuation Methods
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            2. Price-Yield Relationship
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Inverse Relationship
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Price Sensitivity
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Yield Curve Risk
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                2. Deterministic Cash Flow Analysis
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Net Present Value
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Definition and Calculation
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Decision Rules
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Limitations
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        2. Internal Rate of Return
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Definition and Calculation
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Multiple IRRs
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Modified IRR
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              2. Project Appraisal
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Investment Criteria
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Risk Assessment
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Sensitivity Analysis
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Decision Making
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    2. Asset-Liability Management
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Duration
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Macaulay Duration
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Modified Duration
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Key Rate Duration
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Portfolio Duration
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              2. Convexity
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Definition and Calculation
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Positive and Negative Convexity
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Portfolio Convexity
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    2. Immunization
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1. Classical Immunization
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1. Contingent Immunization
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          1. Horizon Matching
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1. Risk Minimization
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            2. Matching Strategies
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1. Cash Flow Matching
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                1. Duration Matching
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1. Convexity Matching
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1. Dynamic Strategies

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