This book is different from all other books on Life Insurance by at least one of the following characteristics 1-4. 1. The treatment of life insurances at three different levels: time-capital, present value and price level. We call time-capital any distribution of a capital over time: (*) is the time-capital with amounts Cl, ~, ... , C at moments Tl, T , ..- , T resp. N 2 N For instance, let (x) be a life at instant 0 with future lifetime X. Then the whole oO oO life insurance A is the time-capital (I,X). The whole life annuity ä is the x x time-capital (1,0) + (1,1) + (1,2) + ... + (I,'X), where 'X is the integer part ofX. The present value at 0 of time-capital (*) is the random variable T1 T TN Cl V + ~ v , + ... + CNV . (**) In particular, the present value ofA 00 and ä 00 is x x 0 0 2 A = ~ and ä = 1 + v + v + ... + v'X resp. x x The price (or premium) of a time-capital is the expectation of its present value. In particular, the price ofA 00 and äx 00 is x 2 A = E(~) and ä = E(I + v + v + ... + v'X) resp.
List of Figures and Tables. Preface. A Guide to Terminology and Notation. 1. Financial Models. 2. Mortality Models. 3. Construction of Life Tables. 4. Basic Concepts of Life Insurance Mathematics. 5. Life Annuities (One Life). 6. Life Insurances (One Life). 7. Relations Between Life Annuities and Life Insurances (One Life). 8. Decompositions of Time-Capitals (One Life). 9. Life Insurance Contracts (One Life). 10. Ruin Probability of a Life Insurance Company. 11. Insurances on a Status (Several Lives). 12. Decomposition of Time-Capitals (Several Lives). 13. Life Insurance Contracts (Several Lives). 14. Multiple Decrement Models. 15. Variances (Several Lives). 16. Population Groups on a Graph. Appendix A: Summation by Parts. Appendix B: Linear Interpolations. Appendix C: Probability Theory. Appendix D: A Differential Equation. Appendix E: Inversion of a Power Series. Appendix F: Summary of Formulas. References. Notation Index. Subject Index.
Inhaltsverzeichnis
List of Figures and Tables. Preface. A Guide to Terminology and Notation. 1. Financial Models. 2. Mortality Models. 3. Construction of Life Tables. 4. Basic Concepts of Life Insurance Mathematics. 5. Life Annuities (One Life). 6. Life Insurances (One Life). 7. Relations Between Life Annuities and Life Insurances (One Life). 8. Decompositions of Time-Capitals (One Life). 9. Life Insurance Contracts (One Life). 10. Ruin Probability of a Life Insurance Company. 11. Insurances on a Status (Several Lives). 12. Decomposition of Time-Capitals (Several Lives). 13. Life Insurance Contracts (Several Lives). 14. Multiple Decrement Models. 15. Variances (Several Lives). 16. Population Groups on a Graph. Appendix A: Summation by Parts. Appendix B: Linear Interpolations. Appendix C: Probability Theory. Appendix D: A Differential Equation. Appendix E: Inversion of a Power Series. Appendix F: Summary of Formulas. References. Notation Index. Subject Index.
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