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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 tim...

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Autor principal: Vylder, F Etienne
Lenguaje:eng
Publicado: Springer 1997
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-1-4757-2616-9
http://cds.cern.ch/record/2006163
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author Vylder, F Etienne
author_facet Vylder, F Etienne
author_sort Vylder, F Etienne
collection CERN
description 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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spelling cern-20061632021-04-21T20:23:47Zdoi:10.1007/978-1-4757-2616-9http://cds.cern.ch/record/2006163engVylder, F EtienneLife insurance theory: actuarial perspectivesMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:20061631997
spellingShingle Mathematical Physics and Mathematics
Vylder, F Etienne
Life insurance theory: actuarial perspectives
title Life insurance theory: actuarial perspectives
title_full Life insurance theory: actuarial perspectives
title_fullStr Life insurance theory: actuarial perspectives
title_full_unstemmed Life insurance theory: actuarial perspectives
title_short Life insurance theory: actuarial perspectives
title_sort life insurance theory: actuarial perspectives
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-1-4757-2616-9
http://cds.cern.ch/record/2006163
work_keys_str_mv AT vylderfetienne lifeinsurancetheoryactuarialperspectives