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Full Description
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.
Contents
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.
