人寿保险数学 (第3版)

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 today's 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. 　　本书为英文版。

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