人壽保險數學(第3版)（簡體書）

Two major developments have influenced the environment of actuarial math-ematics. One is the arrival of powerful and affordable computers; the onceimportant problem of numerical calculation has become almost trivial in many instances. The other is the fact that todays generation is quite familiar with probability theory in an intuitive sense; the basic concepts of probability theory are taught at man), high schools. These two factors should be taken into account in the teaching and learning of actuarial mathematics. A first consequence is, for example, that a recursive algorithm (for a solution) is as useful as a solution expressed in terms of commutation functions. In many cases the calculations are easy; thus the question why a calculation is done is much more important than the question how it is done. The second consequence is that the somewhat embarrassing deterministic model can be abandoned; nowadays nothing speaks against the use of the stochastic model, which better reflects the mechanisms of insurance. Thus the discussion does not have to be limited to expected values; it can be extended to the deviations from the expected values, thereby quantifying the risk in the proper sense.

1 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
2 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
3 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
4 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
5 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
6 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
7 Multiple Decrementsl
8 Multiple Life Insurance
9 The Total Claim Amount in a Portfolio
10 Expense Loadings
11 Estimating Probabilities of Death
Appendix A. Commutation Functions
Appendix B. Simple Interest
Appendix C. Exercises
Appendix D. Solutions
Appendix E. Tables
References
Index