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Life Insurance Theory : Actuarial Perspectives - F. Etienne De Vylder

Life Insurance Theory

Actuarial Perspectives

Hardcover

Published: 31st August 1997
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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 Modelsp. 1
Mortality Modelsp. 11
Construction of Life Tablesp. 19
Basic Concepts of Life Insurance Mathematicsp. 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 Companyp. 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 Modelsp. 115
Variances (Several Lives)p. 133
Population Groups on a Graphp. 139
Summation by Partsp. 157
Linear Interpolationsp. 159
Probability Theoryp. 163
A Differential Equationp. 169
Inversion of a Power Seriesp. 171
Summary of Formulasp. 173
Referencesp. 175
Notation Indexp. 177
Subject Indexp. 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