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Life Insurance Theory

Actuarial Perspectives

  • F. Etienne De Vylder

Table of contents

  1. Front Matter
    Pages i-xv
  2. F. Etienne De Vylder
    Pages 1-10
  3. F. Etienne De Vylder
    Pages 11-17
  4. F. Etienne De Vylder
    Pages 19-24
  5. F. Etienne De Vylder
    Pages 25-28
  6. F. Etienne De Vylder
    Pages 29-41
  7. F. Etienne De Vylder
    Pages 43-50
  8. F. Etienne De Vylder
    Pages 57-64
  9. F. Etienne De Vylder
    Pages 65-81
  10. F. Etienne De Vylder
    Pages 83-94
  11. F. Etienne De Vylder
    Pages 95-103
  12. F. Etienne De Vylder
    Pages 105-109
  13. F. Etienne De Vylder
    Pages 111-113
  14. F. Etienne De Vylder
    Pages 115-132
  15. F. Etienne De Vylder
    Pages 133-138
  16. F. Etienne De Vylder
    Pages 139-156
  17. Back Matter
    Pages 157-184

About this book

Introduction

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.

Keywords

development differential equation evaluation insurance mathematics population portfolio probability probability theory research science and technology statistical method value-at-risk

Authors and affiliations

  • F. Etienne De Vylder
    • 1
  1. 1.GhentBelgium

Bibliographic information