Newton L. Bowers, Hans U. Gerber, James C. Hickman, Donald A. Jones, Cecil J. Nesbitt-Actuarial Mathematics-Society of Actuaries (1997).pdf

Bowers.pdfPortadaPrefaceTable of ContentsAuthor's BiographiesAuthor's Introductions And Guide to StudyIntroduction to Second EditionGuide to Study

1. The Economics of Insurance1.1 Introduction1.2 Utility Theory1.3 Insurance and Utility1.4 Elements of Insurance1.5 Optimal Insurance1.6 Notes and ReferencesAppendixExercises

2. Individual Risk Models for a Short Term2.1 Introduction2.2 Models for Individual Claim Random Variables2.3 Sums of Independent Random Variables2.4 Approximations for the Distribution of the Sum2.5 Applications to Insurance2.6 Notes and ReferencesExercises

3. Survival Distributions and Life Tables3.1 Introduction3.2 Probability for the Age-at-Death3.2.1 The Survival Function3.2.2 Time-until-Death for a Person Age X3.2.3 Curtate-Future-Lifetimes3.2.4 Force of Mortality

3.3 Life Tables3.3.1 Relation of Life Table Functions to the Survival Function3.3.2 Life Table Example

3.4 The Deterministic Survivorship Group3.5 Other Life Table Characteristics3.5.1 Characteristics3.5.2 Recursion Formulas

3.6 Assumptions for Fractional Ages3.7 Some Analytical Laws of Mortality3.8 Select and Ultimate Tables3.9 Notes and ReferencesExercises

4. Life Insurance4.1 Introduction4.2 Insurances Payable at the Moment of Death4.2.1 Level Benefit Insurance4.2.2 Endowment Insurance4.2.3 Deferred Insurance

4.3 Insurances Payable at the End of the Year of Death4.4 Relationships between Insurances Payable at the Moment of Death and the End of the Year of Death4.5 Differencial Equations for Insurances Payable at the Moment of Death4.6 Notes and ReferencesExercises

5. Life Annuities5.1 Introduction5.2 Continuous Life Annuities5.3 Discrete Life Annuities5.4 Life Annuities with m- thly Payments5.5 Apportionable Annuities-Due and Complete Annuities-Immediate5.6 Notes and ReferencesExercises

6. Benefit Premiums6.1 Introduction6.2 Fully Continuous Premiums6.3 Fully Discrete Premiums6.4 True m-thly Payment Premiums6.5 Apportionable Premiums6.6 Accumulation-Type Benefits6.7 Notes and ReferencesExercises

7. Benefit Reserves7.1 Introduction7.2 Fully Continuous Benefit Reserves7.3 Other Formulas for Fully Continuous Benefit Reserves7.4 Fully Discrete Benefit Reserves7.5 Benefit Reserves on a Semicontinuous Basis7.6 Benefit Reserves Based on True m-thly Benefit Premiums7.7 Benefit Reserves on an Apportionable or Discounted Continuous Basis 7.8 Notes and ReferencesExercises

8. Analysis of Benefit Reserves8.1 Introduction8.2 Benefit Reserves for General Insurances8.3 Recursion Relations for Fully Discrete Benefit Reserves8.4 Benefit Reserves at Fractional Durations8.5 Allocation of the Risk to Insurance Years8.6 Differential Equations for Fully Continuous Benefit Reserves8.7 Notes and ReferencesExercises

9. Multiple Life Functions9.1 Introduction9.2 Joint Distributions of Future Lifetimes9.3 The Joint-Life Status9.4 The Last-Survivor Status9.5 More Probabilities and Expectations9.6 Dependent Lifetime Models9.6.1 Common Shock9.6.2 Copulas

9.7 Insurance and Annuity Benefits9.7.1 Survival Statuses9.7.2 Special Two-Life Annuities9.7.3 Reversionary Annuities

9.8 Evaluation - Special Mortality Assumptions9.8.1 Gompertz and Makeham Laws9.8.2 Uniform Distribution

9.9 Simple Contingent Functions9.10 Evaluation- Simple Contingent Functions9.11 Notes and ReferencesExercises

10. Multiple Decrement Models10.1 Introduction10.2 Two Random Variables10.3 Random Survivorship Group10.4 Deterministic Survivorship Group10.5 Associated Single Decrement Tables10.5.1 Basic Relationships10.5.2 Central Rates of Multiple Decrement10.5.3 Constant Force Assumption for Multiple Decrements10.5.4 Uniform Distribution Assumption for Multiple Decrements10.5.5 Estimation Issues

10.6 Construction of a Multiple Decrement Table10.7 Notes and ReferencesExercises

11. Applications of Multiple Decrement Theory11.1 Introduction11.2 Actuarial Present Values and Their Numerical Evaluation11.3 Benefit Premiums and Reserves11.4 Withdrawal Beneft Patterns That Can Be Ignored in Evaluating Premiums and Reserves11.5 Valuation of Pension Plans11.5.1 Demographic Assumptions11.5.2 Projecting Benefit Payment and Contribution Rates11.5.3 Defined - Benefit Plans11.5.4 Defined - Contribution Plans

11.6 Disability Benefits with Individual Life Insurance11.6.1 Disability Income Benefits11.6.2 Waiver-of-Premium Benefits11.6.3 Benefit Premiums and Reserves

11.7 Notes and ReferencesExercises

12. Collective Risk Models for a Single Period12.1 Introduction12.2 The Distribution of Aggregate Claims12.3 Selection of Basic Distributions12.3.1 The Distribution of N12.3.2 The Individual Claim amount Distribution

12.4 Properties of Certain Compound Distributions12.5 Approximations to the Distribution of Aggregate Claims12.6 Notes and ReferencesAppendixExercises

13. Collective Risk Models over an Extended Period13.1 Introduction13.2 A Discrete Time Model13.3 A Continuous Time Model13.4 Ruin Probabilities and the Claim Amount Distribution13.5 The First Surplus below the Initial Level13.6 The Maximal Aggregate Loss13.7 Notes and ReferencesAppendixExercises

14. Applications of Risk Theory14.1 Introduction14.2 Claim Amount Distributions14.3 Approximating the Individual Model14.4 Stop-Loss Reinsurance14.5 Analysis of Reinsurance Using Ruin Theory14.6 Notes and ReferencesAppendixExercises

15. Insurance Models Including Expenses15.1 Introduction15.2 Expense Augmented Models15.2.1 Premiums and Reserves15.2.2 Accounting

15.3 Withdrawal Benefits15.3.1 Premiums and Reserves15.3.2 Accounting

15.4 Types of Expenses15.5 Algebraic Foundations of Accounting: Single Decrement Model15.6 Asset Shares15.6.1 Recursion Relations15.6.2 Accounting

15.7 Expenses, Reserves, and General Insurances15.8 Notes and ReferencesExercises

16. Business and Regulatory Considerations16.1 Introduction16.2 Cash Values16.3 Insurance Options16.3.1 Paid-up Insurance16.3.2 Extended Term16.3.3 Automatic Premium Loan

16.4 Premiums and Economic Considerations16.4.1 Natural Permiums16.4.2 Fund Objective16.4.3 Rate of Return Objective16.4.4 Risk-Based Objectives

16.5 Experience Adjustments16.6 Modified Reserve Methods16.7 Full Preliminary Term16.8 Modified Preliminary Term16.9 Nonlevel Premiums or Benefits16.9.1 Valuation16.9.2 Cash Values


17. Special Annuities and Insurances17.1 Introduction17.2 Special Types of Annuity Benefits17.3 Family Income Insurances17.4 Variable Products17.4.1 Variable Annuity17.4.2 Fully Variable Life Insurance17.4.3 Fixed Premium Variable Life Insurance17.4.4 Paid-up Insurance Increments

17.5 Flexible Plan Products17.5.1 Flexible Plan Illustration17.5.2 An Alternative Design

17.6 Accelerated Benefits17.6.1 Lump Sum Benefits17.6.2 Income Benefits


18. Advanced Multiple Life Theory18.1 Introduction18.2 More General Statuses18.3 Compound Statuses18.4 Contingent Probabilities and Insurances18.5 Compound Contingent Functions18.6 More Reversionary Annuities18.7 Benefit Premiums and Reserves18.8 Notes and ReferencesAppendixExercises

19. Population Theory19.1 Introduction19.2 The Lexis Diagram19.3 A Continuous Model19.4 Stationary and Stable Populations19.5 Acturarial Applications19.6 Population Dynamics19.7 Notes and ReferencesExercises

20. Theory of Pension Funding20.1 Introduction20.2 The Model20.3 Terminal Funding20.4 Basic Functions for Retired Lives20.4.1 Actuarial Present Value of Future Benefits20.4.2 Benefit Payment Rate20.4.3 The Allocation Equation

20.5 Accrual of Actuarial Liability20.6 Basic Functions for Active Lives20.6.1 Acturarial Present Value of Future Benefits20.6.2 Normal Cost Rate20.6.3 Acturarial Accrued Liability20.6.4 Actuarial Present Value of Future Normal Costs

20.7 Individual Acturarial Cost Methods20.8 Group Acturarial Cost Methods20.9 Basic Functions for Active and Retired Members Combined20.10 Notes and ReferencesExercises

21. Interest as a Random Value21.1 Introduction21.1.1 Incorporating Variablity of Interest21.1.2 Notation and Preliminaries

21.2 Scenarios21.2.1 Deterministic Scenarios21.2.2 Random Scenarios: Deterministic Interest Rates

21.3 Independent Interest Rates21.4 Dependet Interest Rates21.4.1 Moving Average Model21.4.2 Implementation

21.5 Financial Economics Models21.5.1 Information in Prices and Maturities21.5.2 Stochastic Models

21.6 Managment of Interest Risk21.6.1 Immunization21.6.2 General Stochastic Model


Appendix 1 Normal Distribution TableAppendix 2A Illustrative Life TableAppendix 2B Illustrative Service TableAppendix 3 Symbol Index Appendix 4 General Rules for Symbols of Actuarial FunctionsAppendix 5 Some Mathematical Formulas Useful in Actuarial MathematicsAppendix 6 BibliographyAppendix 7 Answers to ExercisesIndex

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Newton L. Bowers, Hans U. Gerber, James C. Hickman, Donald A. Jones, Cecil J. Nesbitt-Actuarial Mathematics-Society of Actuaries (1997).pdf