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Three Methods to Calculate the Probability of Ruin

Published online by Cambridge University Press:  29 August 2014

François Dufresne  and
Hans U. Gerber
François Dufresne*
Affiliation:
University of Lausanne, Switzerland
Hans U. Gerber*
Affiliation:
University of Lausanne, Switzerland
*
École des H.E.C., Université de Lausanne, CH-1015 Lausanne, Switzerland.
École des H.E.C., Université de Lausanne, CH-1015 Lausanne, Switzerland.
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Abstract

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The first method, essentially due to GOOVAERTS and DE VYLDER, uses the connection between the probability 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 ruindiscretizationcombination of exponentialssimulation
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 19 , Issue 1 , April 1989 , pp. 71 - 90
Copyright
Copyright © International Actuarial Association 1989

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