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# Life Insurance Theory

### Actuarial Perspectives

Hardcover Published: 31st August 1997
ISBN: 9780792399957
Number Of Pages: 184

### Hardcover

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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 a 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 a 00 is x x 0 0 2 A = ~ and a = 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 ax 00 is x 2 A = E(~) and a = E(I + v + v + ... + v'X) resp.

 List of Figures and Tables Preface A Guide to Terminology and Notation Financial Models p. 1 Mortality Models p. 11 Construction of Life Tables p. 19 Basic Concepts of Life Insurance Mathematics p. 25 Life Annuities (One Life) p. 29 Life Insurances (One Life) p. 43 Relations Between Life Annuities and Life Insurances (One Life) p. 51 Decompositions of Time-Capitals (One Life) p. 57 Life Insurance Contracts (One Life) p. 65 Ruin Probability of a Life Insurance Company p. 83 Insurances on a Status (Several Lives) p. 95 Decomposition of Time-Capitals (Several Lives) p. 105 Life Insurance Contracts (Several Lives) p. 111 Multiple Decrement Models p. 115 Variances (Several Lives) p. 133 Population Groups on a Graph p. 139 Summation by Parts p. 157 Linear Interpolations p. 159 Probability Theory p. 163 A Differential Equation p. 169 Inversion of a Power Series p. 171 Summary of Formulas p. 173 References p. 175 Notation Index p. 177 Subject Index p. 181 Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792399957
ISBN-10: 0792399951
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 184
Published: 31st August 1997
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.4 x 15.6  x 1.91
Weight (kg): 1.03