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 , ..โ{128}ข , 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 รค 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 รค 00 is x x 0 0 2 A = ̃ and รค = 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 รคx 00 is x 2 A = E(̃) and รค = E(I + v + v + ... + v'X) resp
CONTENT
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
