# Three methods to calculate the probability of ruin

### Details

Serval ID

serval:BIB_9B215A737265

Type

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

Collection

Publications

Fund

Title

Three methods to calculate the probability of ruin

Journal

ASTIN Bulletin

Publication state

Published

Issued date

1989

Volume

19

Number

1

Pages

71-90

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.

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.

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Create date

19/11/2007 10:42

Last modification date

03/03/2018 18:53