Life Insurance Theory

Actuarial Perspectives

• F. Etienne De Vylder
Book

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 51-56
9. F. Etienne De Vylder
Pages 57-64
10. F. Etienne De Vylder
Pages 65-81
11. F. Etienne De Vylder
Pages 83-94
12. F. Etienne De Vylder
Pages 95-103
13. F. Etienne De Vylder
Pages 105-109
14. F. Etienne De Vylder
Pages 111-113
15. F. Etienne De Vylder
Pages 115-132
16. F. Etienne De Vylder
Pages 133-138
17. F. Etienne De Vylder
Pages 139-156
18. Back Matter
Pages 157-184

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

• DOI https://doi.org/10.1007/978-1-4757-2616-9
• Copyright Information Springer-Verlag US 1997
• Publisher Name Springer, Boston, MA
• eBook Packages
• Print ISBN 978-1-4419-5189-2
• Online ISBN 978-1-4757-2616-9
• Buy this book on publisher's site