(Ebook) Financial and Actuarial Statistics An Introduction 2nd Edition by Dale S Borowiak, Arnold F Shapiro ISBN 1420085808 9781420085808

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 Nonnegative Random Variables

1.6.1 Pareto Distribution

1.6.2 Lognormal Distribution

1.6.3 Weibull Distribution

1.6.4 Gompertz Distribution

1.6.5 Makeham Distribution

1.7 Conditional Distributions

1.8 Joint Distributions

Problems

Excel Problems

Solutions

2 Statistical Techniques

2.1 Sampling Distributions and Estimation

2.1.1 Point Estimation

2.1.2 Confidence Intervals

2.1.3 Percentiles and Prediction Intervals

2.1.4 Confidence and Prediction Sets

2.2 Sums of Independent Variables

2.3 Order Statistics and Empirical Prediction Intervals

2.4 Approximating Aggregate Distributions

2.4.1 Central Limit Theorem

2.4.2 Haldane Type A Approximation

2.4.3 Saddlepoint Approximation

2.5 Compound Aggregate Variables

2.5.1 Expectations of Compound Aggregate Variables

2.5.2 Limiting Distributions for Compound Aggregate Variables

2.6 Regression Modeling

2.6.1 Least Squares Estimation

2.6.2 Regression Model-Based Inference

2.7 Autoregressive Systems

2.8 Model Diagnostics

2.8.1 Probability Plotting

2.8.2 Generalized Least Squares Diagnostic

2.8.3 Interval Data Diagnostic

Problems

Excel Problems

Solutions

3 Financial Computational Models

3.1 Fixed Financial Rate Models

3.1.1 Financial Rate-Based Calculations

3.1.2 General Period Discrete Rate Models

3.1.3 Continuous-Rate Models

3.2 Fixed-Rate Annuities

3.2.1 Discrete Annuity Models

3.2.2 Continuous Annuity Models

3.3 Stochastic Rate Models

3.3.1 Discrete Stochastic Rate Model

3.3.2 Continuous Stochastic Rate Models

3.3.3 Discrete Stochastic Annuity Models

3.3.4 Continuous Stochastic Annuity Models

Problems

Excel Problems

Solutions

4 Deterministic Status Models

4.1 Basic Loss Model

4.1.1 Deterministic Loss Models

4.1.2 Stochastic Rate Models

4.2 Stochastic Loss Criterion

4.2.1 Risk Criteria

4.2.2 Percentile Criteria

4.3 Single-Risk Models

4.3.1 Insurance Pricing

4.3.2 Investment Pricing

4.3.3 Options Pricing

4.3.4 Option Pricing Diagnostics

4.4 Collective Aggregate Models

4.4.1 Fixed Number of Variables

4.4.2 Stochastic Number of Variables

4.4.3 Aggregate Stop-Loss Reinsurance and Dividends

4.5 Stochastic Surplus Model

4.5.1 Discrete Surplus Model

4.5.2 Continuous Surplus Model

Problems

Excel Problems

Solutions

5 Future Lifetime Random Variables and Life Tables

5.1 Continuous Future Lifetime

5.2 Discrete Future Lifetime

5.3 Force of Mortality

5.4 Fractional Ages

5.5 Select Future Lifetimes

5.6 Survivorship Groups

5.7 Life Models and Life Tables

5.8 Life Table Confidence Sets and Prediction Intervals

5.9 Life Models and Life Table Parameters

5.9.1 Population Parameters

5.9.2 Aggregate Parameters

5.9.3 Fractional Age Adjustments

5.10 Select and Ultimate Life Tables

Problems

Excel Problems

Solutions

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

6.6.3 Relations among Annuity Expectations

6.7 Actuarial Life Tables

6.8 Loss Models and Insurance Premiums

6.8.1 Unit Benefit Premium Notation

6.8.2 Variance of the Loss Function

6.9 Reserves

6.9.1 Unit Benefit Reserves Notations

6.9.2 Relations among Reserve Calculations

6.9.3 Survivorship Group Approach to Reserve Calculations

6.10 General Time Period Models

6.10.1 General Period Expectation

6.10.2 Relations among General Period Expectations

6.11 Expense Models and Computations

Problems

Excel Problems

Solutions

7 Advanced Stochastic Status Models

7.1 Multiple Future Lifetimes

7.1.1 Joint Life Status

7.1.2 Last Survivor Status

7.1.3 General Contingent Status

7.2 Multiple-Decrement Models

7.2.1 Continuous Multiple Decrements

7.2.2 Forces of Decrement

7.2.3 Discrete Multiple Decrements

7.2.4 Single-Decrement Probabilities

7.2.5 Uniformly Distributed Single-Decrement Rates

7.2.6 Single-Decrement Probability Bounds

7.2.7 Multiple-Decrement Life Tables

7.2.8 Single-Decrement Life Tables

7.2.9 Multiple-Decrement Computations

7.3 Pension Plans

7.3.1 Multiple-Decrement Benefits

7.3.2 Pension Contributions

7.3.3 Future Salary-Based Benefits and Contributions

7.3.4 Yearly Based Retirement Benefits

Problems

Excel Problems

Solutions

8 Markov Chain Methods

8.1 Introduction to Markov Chains

8.2 Nonhomogeneous Stochastic Status Chains

8.2.1 Single-Decrement Chains

8.2.2 Actuarial Chains

8.2.3 Multiple-Decrement Chains

8.2.4 Multirisk Strata Chains

8.3 Homogeneous Stochastic Status Chains

8.3.1 Expected Curtate Future Lifetime

8.3.2 Actuarial Chains

8.4 Survivorship Chains

8.4.1 Single-Decrement Models

8.4.2 Multiple-Decrement Models

8.4.3 Multirisk Strata Models

Problems

Excel Problems

Solutions

9 Scenario and Simulation Testing

9.1 Scenario Testing

9.1.1 Deterministic Status Scenarios

9.1.2 Stochastic Status Scenarios

9.1.3 Stochastic Rate Scenarios

9.2 Simulation Techniques

9.2.1 Bootstrap Sampling

9.2.2 Simulation Sampling

9.2.3 Simulation Probabilities

9.2.4 Simulation Prediction Intervals

9.3 Investment Pricing Applications

9.4 Stochastic Surplus Application

9.5 Future Directions in Simulation Analysis

Problems

Excel Problems

Solutions

10 Further Statistical Considerations

10.1 Mortality Adjustment Models

10.1.1 Linear Mortality Acceleration Models

10.1.2 Mean Mortality Acceleration Models

10.1.3 Survival-Based Mortality Acceleration Models

10.2 Mortality Trend Modeling

10.3 Actuarial Statistics

10.3.1 Normality-Based Prediction Intervals

10.3.2 Prediction Set-Based Prediction Intervals

10.3.3 Simulation-Based Prediction Intervals

10.4 Data Set Simplifications

Problems

Excel Problems

Solutions

Appendix A: Excel Statistical Functions, Basic Mathematical Functions, and Add-Ins

Excel Statistical Functions

Excel Basic Mathematical Functions

Excel Add-Ins: Enable Descriptive Statistics, Data Analysis, and Solver

Appendix B: Acronyms and Principal Sections

References

Symbol Index

Index