# Three methods to calculate the probability of ruin

## Details

Serval ID

serval:BIB_F9E4C45878CB

Type

**Article**: article from journal or magazin.

Collection

Publications

Institution

Title

Three methods to calculate the probability of ruin

Journal

ASTIN Bulletin

ISSN

0515-0361

Publication state

Published

Issued date

1989

Peer-reviewed

Oui

Volume

19

Number

1

Pages

71-90

Language

english

Abstract

The first method, essentmlly due to GOOVAERTS and DE VYLDER, uses the connection between the probabiliy of ruin and the maximal aggregate loss random variable, and the fact that the latter has a compound geometric distribution. For the second method, the claim amount distribution is supposed to be a combination of exponential or translated exponential distributions. Then the probability of ruin can be calculated in a transparent fashion; the main problem is to determine the nontrivial roots of the equation that defines the adjustment coefficient. For the third method one observes that the probability of ruin is related to the stationary distribution of a certain associated process. Thus it can be determined by a single simulation of the latter. For the second and third methods the assumption of only proper (positive) claims is not needed.

Keywords

Probability of ruin, discretizatlon, combination of exponentials, simulation

Publisher's website

Create date

19/11/2007 11:55

Last modification date

20/08/2019 17:25