Actuarial Science

  1. Actuarial Models for Losses and Risks
    1. Loss Frequency Models
      1. The (a,b,0) Class of Distributions
        1. Definition and Properties
          1. Recursive Relationships
            1. Parameter Estimation
            2. Poisson Model
              1. Definition and Properties
                1. Parameter Estimation
                  1. Goodness of Fit
                    1. Applications in Claim Counting
                    2. Negative Binomial Model
                      1. Definition and Properties
                        1. Parameter Estimation
                          1. Overdispersion
                          2. Binomial Model
                            1. Definition and Properties
                              1. Parameter Estimation
                                1. Limitations
                                2. Zero-Truncated and Zero-Modified Models
                                  1. Zero-Truncated Distributions
                                    1. Zero-Inflated Distributions
                                      1. Zero-Modified Distributions
                                      2. Model Selection and Fitting
                                        1. Goodness of Fit Tests
                                          1. Information Criteria
                                            1. Cross-Validation
                                              1. Model Comparison
                                            2. Loss Severity Models
                                              1. Parametric Distributions for Severity
                                                1. Exponential Distribution
                                                  1. Properties and Applications
                                                    1. Parameter Estimation
                                                      1. Goodness of Fit
                                                        1. Limitations
                                                        2. Pareto Distribution
                                                          1. Type I and Type II Pareto
                                                            1. Properties and Applications
                                                              1. Parameter Estimation
                                                                1. Heavy-Tailed Characteristics
                                                                2. Lognormal Distribution
                                                                  1. Properties and Applications
                                                                    1. Parameter Estimation
                                                                      1. Relationship to Normal
                                                                        1. Applications in Financial Losses
                                                                        2. Weibull Distribution
                                                                          1. Properties and Applications
                                                                            1. Parameter Estimation
                                                                              1. Hazard Function
                                                                              2. Gamma Distribution
                                                                                1. Properties and Applications
                                                                                  1. Parameter Estimation
                                                                                    1. Special Cases
                                                                                  2. Model Fitting and Selection
                                                                                    1. Method of Moments
                                                                                      1. Maximum Likelihood Estimation
                                                                                        1. Graphical Methods
                                                                                          1. Model Selection Criteria
                                                                                          2. Policy Modifications
                                                                                            1. Deductibles
                                                                                              1. Ordinary Deductibles
                                                                                                1. Franchise Deductibles
                                                                                                  1. Effect on Severity Distribution
                                                                                                  2. Policy Limits
                                                                                                    1. Effect on Severity Distribution
                                                                                                      1. Censoring and Truncation
                                                                                                        1. Parameter Estimation
                                                                                                        2. Coinsurance
                                                                                                          1. Proportional Coverage
                                                                                                            1. Effect on Severity Distribution
                                                                                                              1. Risk Sharing
                                                                                                              2. Inflation Adjustment
                                                                                                                1. Inflation Models
                                                                                                                  1. Trend Factors
                                                                                                                    1. Parameter Adjustment
                                                                                                                2. Aggregate Loss Models
                                                                                                                  1. Collective Risk Model
                                                                                                                    1. Model Structure
                                                                                                                      1. Frequency and Severity Components
                                                                                                                        1. Independence Assumptions
                                                                                                                        2. Individual Risk Model
                                                                                                                          1. Model Structure
                                                                                                                            1. Bernoulli Trials
                                                                                                                              1. Comparison with Collective Model
                                                                                                                              2. Compound Distributions
                                                                                                                                1. Compound Poisson Distribution
                                                                                                                                  1. Definition and Properties
                                                                                                                                    1. Moments
                                                                                                                                      1. Probability Generating Function
                                                                                                                                      2. Compound Binomial Distribution
                                                                                                                                        1. Definition and Properties
                                                                                                                                          1. Moments
                                                                                                                                            1. Comparison with Compound Poisson
                                                                                                                                          2. Recursive Method for Aggregate Claims
                                                                                                                                            1. Panjer Recursion
                                                                                                                                              1. Implementation
                                                                                                                                                1. Computational Considerations
                                                                                                                                                2. Approximations for the Aggregate Distribution
                                                                                                                                                  1. Normal Approximation
                                                                                                                                                    1. Central Limit Theorem Application
                                                                                                                                                      1. Continuity Correction
                                                                                                                                                        1. Accuracy Assessment
                                                                                                                                                        2. Simulation Approaches
                                                                                                                                                          1. Monte Carlo Simulation
                                                                                                                                                            1. Importance Sampling
                                                                                                                                                              1. Variance Reduction
                                                                                                                                                          2. Credibility Theory
                                                                                                                                                            1. Introduction to Credibility
                                                                                                                                                              1. Credibility Concept
                                                                                                                                                                1. Full Credibility
                                                                                                                                                                  1. Partial Credibility
                                                                                                                                                                  2. Bayesian Credibility
                                                                                                                                                                    1. Prior and Posterior Distributions
                                                                                                                                                                      1. Bayesian Updating
                                                                                                                                                                        1. Conjugate Priors
                                                                                                                                                                        2. Bühlmann Credibility
                                                                                                                                                                          1. Model Structure
                                                                                                                                                                            1. Credibility Factor
                                                                                                                                                                              1. Credibility Premium
                                                                                                                                                                              2. Bühlmann-Straub Credibility
                                                                                                                                                                                1. Model Extension
                                                                                                                                                                                  1. Exposure Weighting
                                                                                                                                                                                    1. Credibility Factor
                                                                                                                                                                                    2. Empirical Bayes Methods
                                                                                                                                                                                      1. Parameter Estimation
                                                                                                                                                                                        1. Credibility Factors
                                                                                                                                                                                          1. Comparison with Classical Methods
                                                                                                                                                                                          2. Limited Fluctuation Credibility
                                                                                                                                                                                            1. Full Credibility Standards
                                                                                                                                                                                              1. Partial Credibility
                                                                                                                                                                                                1. Square Root Rule
                                                                                                                                                                                                2. Applications in Ratemaking and Reserving
                                                                                                                                                                                                  1. Experience Rating
                                                                                                                                                                                                    1. Bonus-Malus Systems
                                                                                                                                                                                                      1. Reserve Adequacy
                                                                                                                                                                                                        1. Practical Considerations
                                                                                                                                                                                                      2. Simulation
                                                                                                                                                                                                        1. Monte Carlo Methods
                                                                                                                                                                                                          1. Random Number Generation
                                                                                                                                                                                                            1. Pseudo-Random Numbers
                                                                                                                                                                                                              1. Quasi-Random Numbers
                                                                                                                                                                                                              2. Simulating from Distributions
                                                                                                                                                                                                                1. Inverse Transform Method
                                                                                                                                                                                                                  1. Acceptance-Rejection Method
                                                                                                                                                                                                                    1. Composition Method
                                                                                                                                                                                                                      1. Special Techniques
                                                                                                                                                                                                                      2. Variance Reduction Techniques
                                                                                                                                                                                                                        1. Antithetic Variables
                                                                                                                                                                                                                          1. Control Variables
                                                                                                                                                                                                                            1. Stratified Sampling
                                                                                                                                                                                                                              1. Importance Sampling
                                                                                                                                                                                                                              2. Applications in Actuarial Modeling
                                                                                                                                                                                                                                1. Risk Assessment
                                                                                                                                                                                                                                  1. Capital Modeling
                                                                                                                                                                                                                                    1. Stress Testing
                                                                                                                                                                                                                                      1. Model Validation
                                                                                                                                                                                                                                      2. Model Validation
                                                                                                                                                                                                                                        1. Backtesting
                                                                                                                                                                                                                                          1. Sensitivity Analysis
                                                                                                                                                                                                                                            1. Scenario Testing
                                                                                                                                                                                                                                              1. Performance Metrics

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                                                                                                                                                                                                                                          5. Ratemaking and Reserving for General Insurance