Contents
The Mathematics of Compound Interest
1.1 Mathematical Bases of Life Contingencies
1.2 Effective Interest Rates
1.3 Nominal Interest Rates
1.4 Continuous Payments
1.5 Interest in Advance
1.6 Perpetuities
1.7 Annuities
1.8 Repayment ofa Debt
1.9 Internal Rate of Return
The Future Lifetime of a Life Aged x
2.1 The Model
2.2 The Force of Mortality
2.3 Analytical Distributions of T
2.4 The Curtate Future Lifetime of (x)
2.5 Life Tables
2.6 Probabilities of Death for Fractions of a Year
Life Insurance
3.1 Introduction
3.2 Elementary Insurance Types
3.2.1 Whole Life and Term Insurance
3.2.2 Pure Endowments
3.2.3 Endowments
3.3 Insurances Payable at the Moment of Death
3.4 General Types of Life Insurance
3.5 Standard Types of Variable Life Insurance
3.6 Recursive Formulae
Life Annuities
4.1 Introduction
4.2 Elementary Life Annuities
4.3 Payments made more Frequently than Once a Year
4.4 Variable Life Annuities
4.5 Standard Types of Life Annuituy
4.6 Recursion Formulae
4.7 Inequalities
4.8 Payments Starting at Non-iutegral Ages
Net Premiums
5.1 Introduction
5.2 An Example
5.3 Elementary Forms of Insurance
5.3.1 Whole Life and Term Insurance
5.3.2 Pure Endowments
5.3.3 Endowments
5.3.4 Deferred Life Annuities
5.4 Premiums Paid m Times a Year
5.5 A General Type of Life Insurance
5.6 Policies with Premium Refund
5.7 Stochastic Interest
Net Premium Reserves
6.1 Introduction
6.2 Two Examples
6.3 Recursive Considerations
6.4 The Survival Risk
6.5 The Net Premium Reserve of a Whole Life Insurance
6.6 Net Premium Reserves at Fractional Durations
6.7 Allocation of the Overall Loss to Policy Years
6.8 Conversion of an Insurance
6.9 Technical Gain
6.10 Procedure for Pure Endowments
6.11 The Continuous Model
Multiple Decrements
7.1 The Model
7.2 Forces of Decrement
7.3 The Curtate Lifetime of (x)
7.4 A General Type of Insurance
7.5 The Net Premium Reserve
7.6 The Continuous Model
Multiple Life Insurance
8.1 Introduction
8.2 The Joint-Life Status
8.3 Simplifications
8.4 The Last-Survivor Status
8.5 The General Symmetric Status
8.6 The Schuette-Nesbitt Formula
8.7 Asymmetric Annuities
8.8 Asymmetric Insurances
The Total Claim Amount in a Portfolio
9.1 Introduction
9.2 The Normal Approximation
9.3 Exact Calculation of the Total Claim Amount Distribution
9.4 The Compound Poisson Approximation
9.5 Recursive Calculation of the Compound Poisson Distribution
9.6 Reinsurance
9.7 Stop-Loss Reinsurance
Expense Loadings
10.1 Introduction
10.2 The Expense-Loaded Premium
10.3 Expense-Loaded Premium Reserves
11 Estimating Probabilities of Death
11.1 Problem Description
11.2 The Classical Method
11.3 Alternative Solution
11.4 The Maximum Likelihood Method
11.5 Statistical Inference
11.6 The Bayesian Approach
11.7 Multiple Causes of Decrement
11.8 Interpretation of Results
Appendix A. Commutation Functions
A.l Introduction
A2 The Deterministic Model
A.3 Life Annuities
A.4 Life Insurance
A.5 Net Annual Premiums and Premium Reserves
Appendix B. Simple Interest
Appendix C. Exercises
C.O Introduction
C.l Mathematics of Compound Interest: Exercises
C.l.l Theory Exercises
C.1.2 Spreadsheet Exercses
C.2 The Future Lifetime of a Life Aged x: Exercises
C.2.1 Theory Exercises
C.2.2 Spreadsheet Exercises
C.3 Life Insurance
C.3.1 Theory Exercises
C.3.2 Spre.adsheet Exercises
C.4 Life Annuities
C.4.1 Theory Exercises
C.4.2 Spreadsheet Exercises
C.5 Net Premiums
C.5.1 Notes
C.5.2 Theory Exercises
C.5.3 Spreadsheet Exercises
C.6 Net Premium Reserves
C.6.1 Theory Exercises
C.6.2 Spreadsheet Exercises
C.7 Multiple Decrements: Exercises
C.7.1 Theory Exercises
C.8 Multiple Life Insurance: Exercises
C.8.1 Theory Exercises
C.8.2 Spreadsheet Exercises
C.9 The Total Claim Amount in a Portfolio
C.9.1 Theory Exercises
C.10 Expense Loadings
C.10.1 Theory Exercises
C.10.2 Spreadsheet Exercises
C.11 Estimating Probabilities of Death
C.11.1 Theory Exercises
Apendix D. Solutions
D.0 Introduction
D.l Mathematics of Compound Interest
D.l.l Solutions to Theory Exercises
D.1.2 Solutions to Spreadsheet Exercises
D.2 The Future Lifetime of a Life Aged x
D.2.1 Solutions to Theory Exercise
D.2.2 Solutions to Spreadsheet Exercises
D.3 Life Insurance
D.3.1 Solutions to Theory Exercises
D.3.2 Solution to Spreadsheet Exercises
D.4 Life Annuities
D.4.1 Solutions to Theory Exercises
D.4.2 Solutions to Spreadsheet Exercises
D.5 Net Premiums: Solutions
D.5.1 Theory Exercises
D.5.2 Solutions to Spreadsheet Exercises
D.6 Net Premium Reserves: Solutions
D.6.1 Theory Exercises
D.6.2 Solutions to Spreadsheet Exercises
D.7 Multiple Oecrements: Solutions
D.7.1 Theory Exercises
D.8 . Multiple Life Insurance: Solutions
D.8.1 Theory Exercises
D.8.2 Solutions to Spreadsheet Exercises
D.9 The Total Claim Amount in a Portfolio
D.9.1 Theory Exercises
D.10 Expense Loadings
D.10.1 Theory Exercises
D.10.2 Spreadsheet Exercises
D.11 Estimating Probabilities of Oeath
D.11.1 Theory Exercises
Appendix E. Tables
E.0 Illustrative Life Tables
E.l Commutation Columns
E.2 Multiple Oecrement Tables
References
Index
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