Ebook: Life Insurance Theory: Actuarial Perspectives

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.

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This concise self-contained book on life contingencies is written for students, teachers, researchers and life insurance practitioners. The stochastic model, introduced by Professor De Vylder more than twenty years ago and now widely adopted, is used throughout the monograph. Beyond the classical material of life insurance mathematics, the emphasis lies on variance evaluations of mathematical reserves, allowing the estimation of long term ruin probabilities in life insurance portfolios with varying volume. Other characteristics of the book are its great generality, the inclusion of an axiomatic theory of compound interests, the development of statistical methods for mortality and other estimations, and the introduction of graphs making a clear visualization of multiple decrement models possible. This approach makes the monograph incomparable to other books in the field.

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This concise self-contained book on life contingencies is written for students, teachers, researchers and life insurance practitioners. The stochastic model, introduced by Professor De Vylder more than twenty years ago and now widely adopted, is used throughout the monograph. Beyond the classical material of life insurance mathematics, the emphasis lies on variance evaluations of mathematical reserves, allowing the estimation of long term ruin probabilities in life insurance portfolios with varying volume. Other characteristics of the book are its great generality, the inclusion of an axiomatic theory of compound interests, the development of statistical methods for mortality and other estimations, and the introduction of graphs making a clear visualization of multiple decrement models possible. This approach makes the monograph incomparable to other books in the field.
Content:
Front Matter....Pages i-xv
Financial Models....Pages 1-10
Mortality Models....Pages 11-17
Construction of Life Tables....Pages 19-24
Basic Concepts of Live Insurance Mathematics....Pages 25-28
Life Annuities (One Life)....Pages 29-41
Life Insurances (One Life)....Pages 43-50
Relations between Life Annuities and Life Insurances (One Life)....Pages 51-56
Decompositions of Time-Capitals (One Life)....Pages 57-64
Life Insurance Contracts (One Life)....Pages 65-81
Ruin Probability of a Life Insurance Company....Pages 83-94
Insurances on a Status (Several Lives)....Pages 95-103
Decompositions of Time-Capitals (Several Lives)....Pages 105-109
Life Insurance Contracts (Several Lives)....Pages 111-113
Multiple Decrement Models....Pages 115-132
Variances (Several Lives)....Pages 133-138
Population Groups on a Graph....Pages 139-156
Back Matter....Pages 157-184

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This concise self-contained book on life contingencies is written for students, teachers, researchers and life insurance practitioners. The stochastic model, introduced by Professor De Vylder more than twenty years ago and now widely adopted, is used throughout the monograph. Beyond the classical material of life insurance mathematics, the emphasis lies on variance evaluations of mathematical reserves, allowing the estimation of long term ruin probabilities in life insurance portfolios with varying volume. Other characteristics of the book are its great generality, the inclusion of an axiomatic theory of compound interests, the development of statistical methods for mortality and other estimations, and the introduction of graphs making a clear visualization of multiple decrement models possible. This approach makes the monograph incomparable to other books in the field.
Content:
Front Matter....Pages i-xv
Financial Models....Pages 1-10
Mortality Models....Pages 11-17
Construction of Life Tables....Pages 19-24
Basic Concepts of Live Insurance Mathematics....Pages 25-28
Life Annuities (One Life)....Pages 29-41
Life Insurances (One Life)....Pages 43-50
Relations between Life Annuities and Life Insurances (One Life)....Pages 51-56
Decompositions of Time-Capitals (One Life)....Pages 57-64
Life Insurance Contracts (One Life)....Pages 65-81
Ruin Probability of a Life Insurance Company....Pages 83-94
Insurances on a Status (Several Lives)....Pages 95-103
Decompositions of Time-Capitals (Several Lives)....Pages 105-109
Life Insurance Contracts (Several Lives)....Pages 111-113
Multiple Decrement Models....Pages 115-132
Variances (Several Lives)....Pages 133-138
Population Groups on a Graph....Pages 139-156
Back Matter....Pages 157-184
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