Financial and Actuarial Statistics: An Introduction (Statistics: A Series of Textbooks and Monographs)

Based on a loss function approach, this comprehensive reference reviews the most recent advances in financial and actuarial modeling, providing a strong statistical background for advanced methods in pension plan structuring, risk estimation, and modeling of investment and options pricing. An authoritative tool supplying every conceptual model and technique required by the modern financial investigator, Financial and Actuarial Statistics offers an analysis of American options models, mortality adjustment factors for increased risk individuals, time trend regression adjustments for mortality tables, and simulation approaches for stochastic models. 3.3.3 Options Pricing -- 3.4 Short Time Period Collective Aggregate Models -- 3.4.1 Fixed Number of Variables -- 3.4.2 Stochastic Number of Variables -- 3.4.3 Aggregate Stop - Loss Insurance and Dividends 3.5 Stochastic Surplus Model -- Problems -- 4 Future Lifetime Random Variable -- 4.1 Continuous Future Lifetime -- 4.2 Discrete Future Lifetime -- 4.3 Force of Mortality -- 4.4 Fractional Ages -- 4.5 Multiple Future Lifetimes -- 4.5.1 Joint Life Status -- 4.5.2 Last Survivor Status -- 4.5.3 General Contingent Status -- 4.6 Select Future Lifetimes -- 4.7 Multiple Decrement Lifetimes -- 4.7.1 Continuous Multiple Decrements -- 4.7.2 Forces of Mortality -- 4.7.3 Discrete Multiple Decrements -- 4.7.4 Single Decrement Probabilities -- 4.7.5 Uniformly Distributed Single Decrement Rates -- 4.7.6 Single Decrement Probability Bounds -- Problems -- 5 Future Lifetime Models and Tables -- 5.1 Survivorship Groups -- 5.2 Life Models and Tables -- 5.3 Estimated Life Models and Tables -- 5.4 Life Models and Life Table Parameters -- 5.4.1 Population Parameters -- 5.4.2 Aggregate Parameters -- 5.4.3 Fractional Age Adjustments -- 5.5 Multiple Life Tables and Parameters -- 5.6 Select and Ultimate Life Tables -- 5.7 Multiple Decrement Tables -- 5.7.1 Multiple Decrement Life Tables -- 5.7.2 Single Decrement Life Tables -- Problems -- 6 Stochastic Status Models -- 6.1 Stochastic Present Value Functions -- 6.2 Risk Evaluations -- 6.2.1 Continuous Risk Calculations -- 6.2.2 Discrete Risk Calculations -- 6.2.3 Mixed Risk Calculations -- 6.3 Percentile Evaluations -- 6.4 Life Insurance -- 6.4.1 Types of Unit Benefit Life Insurance -- 6.5 Life Annuities -- 6.5.1 Types of Unit Payment Life Annuities -- 6.5.2 Apportionable Annuities -- 6.6 Relating Risk Calculations -- 6.6.1 Relations Among Insurance Expectations -- 6.6.2 Relations Among Insurance and Annuity Expectations Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Preface -- Contents -- 1 Statistical Concepts -- 1.1 Probability -- 1.2 Random Variables -- 1.2.1 Discrete Random Variables -- 1.2.2 Continuous Random Variables -- 1.2.3 Mixed Random Variables -- 1.3 Expectations -- 1.4 Moment Generating Function -- 1.5 Survival Functions -- 1.6 Conditional Distributions -- 1.7 Joint Distributions -- 1.8 Sampling Distributions and Estimation -- 1.8.1 Point Estimation -- 1.8.2 Percentiles and Prediction Intervals -- 1.8.3 Parameter Interval Estimation -- 1.9 Aggregate Sums of Independent Random Variables 3 -- 1.10 Order Statistics -- 1.11 Approximating Aggregate Sums -- 1.11.1 Central Limit Theorem -- 1.11.2 Haldane Type A Approximation -- 1.11.3 Saddlepoint Approximation -- 1.12 Compound Random Variables -- 1.12.1 Expectations of Compound Variables -- 1.12.2 Limiting Distributions for Compound Variables -- 1.13 Regression Modeling -- 1.13.1 Least Squares Estimation -- 1.13.2 Regression Model Based Inference -- 1.14 Autoregressive Systems -- Problems -- 2 Financial Computational Models -- 2.1 Fixed Financial Rate Models -- 2.1.1 Financial Rate Based Calculations -- 2.1.2 General Period Discrete Rate Models -- 2.1.3 Continuous Rate Models -- 2.2 Fixed Rate Annuities -- 2.2.1 Discrete Annuity Models -- 2.2.2 Continuous Annuity Models -- 2.3 Stochastic Rate Models -- 2.3.1 Discrete Stochastic Rate Model -- 2.3.2 Continuous Stochastic Rate Models -- 2.3.3 Discrete Stochastic Annuity Models -- 2.3.4 Continuous Stochastic Annuity Models -- Problems -- 3 Deterministic Status Models -- 3.1 Basic Loss Model -- 3.1.1 Deterministic Loss Models -- 3.1.2 Stochastic Rate Models -- 3.2 Stochastic Loss Criterion -- 3.2.1 Risk Criteria -- 3.2.2 Percentile Criteria -- 3.3 Single Risk Models -- 3.3.1 Insurance Pricing -- 3.3.2 Investment Pricing 6.6.3 Relations Among Annuity Expectations -- 6.7 Life Table Applications -- 6.8 Insurance Premiums -- 6.8.1 Unit Benefit Premium Notation -- 6.9 Reserves -- 6.9.1 Unit Benefit Reserves Notations -- 6.9.2 Relations Among Reserves Calculations -- 6.9.3 Survivorship Group Approach to Reserve Calculations -- 6.10 General Time Period Models -- 6.10.1 General Period Expectations -- 6.10.2 Relations Among General Period Expectations -- 6.11 Multiple Decrement Computations -- 6.12 Pension Plans -- 6.12.1 Multiple Decrement Benefits -- 6.12.2 Pension Contributions -- 6.12.3 Future Salary Based Benefits and Contributions -- 6.12.4 Yearly Based Retirement Benefits -- 6.13 Models Including Expenses -- Problems -- 7 Scenario and Simulation Testing -- 7.1 Fixed Rate Deterministic Status Models -- 7.2 Simulation Methods -- 7.2.1 Bootstrap Resampling -- 7.2.2 Simulation Sampling -- 7.3 Simulation Inference on Detenninistic Status Models -- 7.4 Simulation Inference on Collective Aggregate Models -- 7.5 Simulation Inference on Stochastic Status Models -- 7.5.1 Investment Pricing Models -- 7.5.2 Stochastic Surplus Models -- 7.6 Further Directions in Resampling -- Problems -- 8 Further Statistical Considerations -- 8.1 Statistical Investigations -- 8.2 Mortality Adjustment Factors -- 8.2.1 Linear Acceleration Factors -- 8.2.2 Mean Acceleration Factors -- 8.2.3 Survival Acceleration Factors -- 8.3 Mortality Trend Modeling -- Problems -- Appendix: Standard Normal Tables -- References -- Index Statistical concepts Financial computational models Deterministic status models Future lifetime random variable Future lifetime models and tables Stochastic status models Scenario and simulation testing Futher statistical considerations. This text reviews advances in financial and actuarial modeling. It offers an analysis of American options models, mortality adjustment factors for increased risk individuals and time trend regression adjustments for mortality tables