Actuarial Science

  1. Life Contingencies and Survival Models
    1. Survival Analysis
      1. Future Lifetime as a Random Variable
        1. Definition of Future Lifetime
          1. Probability Distributions
            1. Moments of Future Lifetime
              1. Applications in Insurance
              2. Survival Function
                1. Definition and Properties
                  1. Relationship to Distribution Function
                    1. Estimation Methods
                      1. Graphical Representation
                      2. Force of Mortality
                        1. Definition and Interpretation
                          1. Relationship to Survival Function
                            1. Hazard Rate Properties
                              1. Age-Specific Mortality
                              2. Life Tables
                                1. Construction of Life Tables
                                  1. Data Requirements
                                    1. Graduation Methods
                                      1. Smoothing Techniques
                                        1. Quality Assessment
                                        2. Cohort vs. Period Life Tables
                                          1. Cohort Life Tables
                                            1. Period Life Tables
                                              1. Advantages and Limitations
                                              2. Select and Ultimate Tables
                                                1. Select Period
                                                  1. Ultimate Rates
                                                    1. Construction Methods
                                                      1. Applications in Underwriting
                                                      2. Graduation of Mortality Rates
                                                        1. Parametric Methods
                                                          1. Non-Parametric Methods
                                                            1. Goodness of Fit Tests
                                                              1. Smoothing Techniques
                                                            2. Fractional Age Assumptions
                                                              1. Uniform Distribution of Deaths
                                                                1. Assumption and Implications
                                                                  1. Interpolation Formulas
                                                                    1. Limitations
                                                                    2. Constant Force of Mortality
                                                                      1. Assumption and Implications
                                                                        1. Exponential Distribution
                                                                          1. Comparison with UDD
                                                                          2. Balducci Assumption
                                                                            1. Assumption and Implications
                                                                              1. Interpolation Formulas
                                                                                1. Comparison with Other Methods
                                                                              2. Curtate Future Lifetime
                                                                                1. Definition and Properties
                                                                                  1. Probability Mass Function
                                                                                    1. Moments
                                                                                  2. Models for Life Insurance
                                                                                    1. Actuarial Present Value
                                                                                      1. Definition and Calculation
                                                                                        1. Random Variables
                                                                                          1. Expected Values
                                                                                            1. Variance Calculations
                                                                                            2. Whole Life Insurance
                                                                                              1. Level Benefit Whole Life
                                                                                                1. Benefit Structure
                                                                                                  1. Present Value Calculations
                                                                                                    1. Premium Calculations
                                                                                                      1. Policy Values
                                                                                                      2. Single Premium Whole Life
                                                                                                        1. Net Single Premium
                                                                                                          1. Gross Single Premium
                                                                                                            1. Comparisons
                                                                                                            2. Annual Premium Whole Life
                                                                                                              1. Net Annual Premium
                                                                                                                1. Gross Annual Premium
                                                                                                                  1. Premium Payment Period
                                                                                                                2. Term Life Insurance
                                                                                                                  1. Level Term Insurance
                                                                                                                    1. Benefit Structure
                                                                                                                      1. Present Value Calculations
                                                                                                                        1. Premium Calculations
                                                                                                                          1. Conversion Options
                                                                                                                          2. Decreasing Term Insurance
                                                                                                                            1. Benefit Structure
                                                                                                                              1. Present Value Calculations
                                                                                                                                1. Premium Calculations
                                                                                                                              2. Endowment Insurance
                                                                                                                                1. Pure Endowment
                                                                                                                                  1. Benefit Structure
                                                                                                                                    1. Present Value Calculations
                                                                                                                                      1. Investment Characteristics
                                                                                                                                      2. Endowment Assurance
                                                                                                                                        1. Combined Benefits
                                                                                                                                          1. Present Value Calculations
                                                                                                                                            1. Premium Calculations
                                                                                                                                          2. Deferred Insurance
                                                                                                                                            1. Deferred Whole Life
                                                                                                                                              1. Deferred Term Insurance
                                                                                                                                                1. Present Value Calculations
                                                                                                                                                2. Varying Benefit Insurance
                                                                                                                                                  1. Increasing Benefits
                                                                                                                                                    1. Arithmetic Increases
                                                                                                                                                      1. Geometric Increases
                                                                                                                                                        1. Present Value Calculations
                                                                                                                                                        2. Decreasing Benefits
                                                                                                                                                          1. Arithmetic Decreases
                                                                                                                                                            1. Geometric Decreases
                                                                                                                                                              1. Present Value Calculations
                                                                                                                                                          2. Models for Life Annuities
                                                                                                                                                            1. Whole Life Annuities
                                                                                                                                                              1. Annuity-Immediate
                                                                                                                                                                1. Benefit Structure
                                                                                                                                                                  1. Present Value Calculations
                                                                                                                                                                    1. Variance Calculations
                                                                                                                                                                    2. Annuity-Due
                                                                                                                                                                      1. Benefit Structure
                                                                                                                                                                        1. Present Value Calculations
                                                                                                                                                                          1. Variance Calculations
                                                                                                                                                                            1. Comparison with Immediate
                                                                                                                                                                          2. Temporary Life Annuities
                                                                                                                                                                            1. Fixed Term Annuities
                                                                                                                                                                              1. Present Value Calculations
                                                                                                                                                                                1. Comparison with Whole Life
                                                                                                                                                                                2. Deferred Life Annuities
                                                                                                                                                                                  1. Deferred Immediate Annuities
                                                                                                                                                                                    1. Deferred Annuities Due
                                                                                                                                                                                      1. Present Value Calculations
                                                                                                                                                                                      2. Annuities with Guaranteed Payments
                                                                                                                                                                                        1. Certain and Life Annuities
                                                                                                                                                                                          1. Benefit Structure
                                                                                                                                                                                            1. Present Value Calculations
                                                                                                                                                                                              1. Risk Characteristics
                                                                                                                                                                                              2. Refund Annuities
                                                                                                                                                                                                1. Cash Refund Annuities
                                                                                                                                                                                                  1. Installment Refund Annuities
                                                                                                                                                                                                    1. Present Value Calculations
                                                                                                                                                                                                2. Net Premiums and Premium Calculation
                                                                                                                                                                                                  1. Equivalence Principle
                                                                                                                                                                                                    1. Definition and Application
                                                                                                                                                                                                      1. Present Value Equivalence
                                                                                                                                                                                                        1. Risk Considerations
                                                                                                                                                                                                          1. Limitations
                                                                                                                                                                                                          2. Net Premiums
                                                                                                                                                                                                            1. Net Single Premiums
                                                                                                                                                                                                              1. Net Annual Premiums
                                                                                                                                                                                                                1. Net Level Premiums
                                                                                                                                                                                                                  1. Calculation Methods
                                                                                                                                                                                                                  2. Annual Premiums
                                                                                                                                                                                                                    1. Level Annual Premiums
                                                                                                                                                                                                                      1. Varying Annual Premiums
                                                                                                                                                                                                                        1. Premium Payment Periods
                                                                                                                                                                                                                        2. Fractional Premiums
                                                                                                                                                                                                                          1. Semi-Annual Premiums
                                                                                                                                                                                                                            1. Quarterly Premiums
                                                                                                                                                                                                                              1. Monthly Premiums
                                                                                                                                                                                                                                1. Approximation Methods
                                                                                                                                                                                                                                2. Return of Premium Policies
                                                                                                                                                                                                                                  1. Return of Premium Term
                                                                                                                                                                                                                                    1. Return of Premium Whole Life
                                                                                                                                                                                                                                      1. Present Value Calculations
                                                                                                                                                                                                                                      2. Gross Premiums
                                                                                                                                                                                                                                        1. Expense Loadings
                                                                                                                                                                                                                                          1. Acquisition Expenses
                                                                                                                                                                                                                                            1. Maintenance Expenses
                                                                                                                                                                                                                                              1. Overhead Expenses
                                                                                                                                                                                                                                                1. Loading Methods
                                                                                                                                                                                                                                                2. Profit Loadings
                                                                                                                                                                                                                                                  1. Profit Margins
                                                                                                                                                                                                                                                    1. Risk Charges
                                                                                                                                                                                                                                                      1. Contingency Reserves
                                                                                                                                                                                                                                                        1. Competitive Considerations
                                                                                                                                                                                                                                                    2. Policy Values and Reserves
                                                                                                                                                                                                                                                      1. Net Premium Reserves
                                                                                                                                                                                                                                                        1. Definition and Purpose
                                                                                                                                                                                                                                                          1. Calculation Methods
                                                                                                                                                                                                                                                            1. Reserve Adequacy
                                                                                                                                                                                                                                                              1. Regulatory Requirements
                                                                                                                                                                                                                                                              2. Prospective and Retrospective Methods
                                                                                                                                                                                                                                                                1. Prospective Reserve Method
                                                                                                                                                                                                                                                                  1. Retrospective Reserve Method
                                                                                                                                                                                                                                                                    1. Equivalence of Methods
                                                                                                                                                                                                                                                                    2. Gross Premium Reserves
                                                                                                                                                                                                                                                                      1. Gross Premium Valuation
                                                                                                                                                                                                                                                                        1. Expense Reserves
                                                                                                                                                                                                                                                                          1. Profit Reserves
                                                                                                                                                                                                                                                                          2. Modified Reserves
                                                                                                                                                                                                                                                                            1. Full Preliminary Term Method
                                                                                                                                                                                                                                                                              1. Commissioners Reserve Valuation Method
                                                                                                                                                                                                                                                                                1. Other Modified Methods
                                                                                                                                                                                                                                                                                2. Surrender Values
                                                                                                                                                                                                                                                                                  1. Cash Surrender Values
                                                                                                                                                                                                                                                                                    1. Reduced Paid-Up Insurance
                                                                                                                                                                                                                                                                                      1. Extended Term Insurance
                                                                                                                                                                                                                                                                                        1. Calculation Methods
                                                                                                                                                                                                                                                                                        2. Policyholder Dividends
                                                                                                                                                                                                                                                                                          1. Dividend Calculation
                                                                                                                                                                                                                                                                                            1. Dividend Options
                                                                                                                                                                                                                                                                                              1. Participating vs. Non-Participating
                                                                                                                                                                                                                                                                                                1. Regulatory Considerations
                                                                                                                                                                                                                                                                                              2. Multiple Life Models
                                                                                                                                                                                                                                                                                                1. Joint Life Status
                                                                                                                                                                                                                                                                                                  1. Joint Survival Probabilities
                                                                                                                                                                                                                                                                                                    1. Joint Life Insurance
                                                                                                                                                                                                                                                                                                      1. Joint Life Annuities
                                                                                                                                                                                                                                                                                                      2. Last Survivor Status
                                                                                                                                                                                                                                                                                                        1. Last Survivor Probabilities
                                                                                                                                                                                                                                                                                                          1. Last Survivor Insurance
                                                                                                                                                                                                                                                                                                            1. Last Survivor Annuities
                                                                                                                                                                                                                                                                                                            2. Contingent Probabilities
                                                                                                                                                                                                                                                                                                              1. Conditional Survival
                                                                                                                                                                                                                                                                                                                1. Order Statistics
                                                                                                                                                                                                                                                                                                                  1. Calculation Methods
                                                                                                                                                                                                                                                                                                                  2. Contingent Insurance and Annuities
                                                                                                                                                                                                                                                                                                                    1. Contingent Life Insurance
                                                                                                                                                                                                                                                                                                                      1. Contingent Annuities
                                                                                                                                                                                                                                                                                                                        1. Reversionary Annuities
                                                                                                                                                                                                                                                                                                                        2. Multiple Life Annuities
                                                                                                                                                                                                                                                                                                                          1. Joint and Survivor Annuities
                                                                                                                                                                                                                                                                                                                            1. Reversionary Annuities
                                                                                                                                                                                                                                                                                                                              1. Contingent Annuities
                                                                                                                                                                                                                                                                                                                            2. Multiple Decrement Models
                                                                                                                                                                                                                                                                                                                              1. Theory of Competing Risks
                                                                                                                                                                                                                                                                                                                                1. Multiple Causes of Decrement
                                                                                                                                                                                                                                                                                                                                  1. Independent Competing Risks
                                                                                                                                                                                                                                                                                                                                    1. Dependent Competing Risks
                                                                                                                                                                                                                                                                                                                                    2. Associated Single Decrement Tables
                                                                                                                                                                                                                                                                                                                                      1. Construction Methods
                                                                                                                                                                                                                                                                                                                                        1. Relationship to Multiple Decrement
                                                                                                                                                                                                                                                                                                                                          1. Limitations
                                                                                                                                                                                                                                                                                                                                          2. Construction of Multiple Decrement Tables
                                                                                                                                                                                                                                                                                                                                            1. Data Requirements
                                                                                                                                                                                                                                                                                                                                              1. Estimation Methods
                                                                                                                                                                                                                                                                                                                                                1. Graduation Techniques
                                                                                                                                                                                                                                                                                                                                                  1. Quality Assessment
                                                                                                                                                                                                                                                                                                                                                  2. Applications in Pension and Insurance
                                                                                                                                                                                                                                                                                                                                                    1. Pension Plan Decrements
                                                                                                                                                                                                                                                                                                                                                      1. Disability Insurance
                                                                                                                                                                                                                                                                                                                                                        1. Group Insurance
                                                                                                                                                                                                                                                                                                                                                          1. Employee Benefits

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                                                                                                                                                                                                                                                                                                                                                      Go to top

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                                                                                                                                                                                                                                                                                                                                                      4. Actuarial Models for Losses and Risks