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On the Probability and Severity of Ruin

Published online by Cambridge University Press:  29 August 2014

Hans U. Gerber ,
Marc J. Goovaerts  and
Rob Kaas
Hans U. Gerber*
Affiliation:
Université de Lausanne
Marc J. Goovaerts*
Affiliation:
K. U. Leuven and University of Amsterdam
Rob Kaas*
Affiliation:
University of Amsterdam
*
Ecole des H.E.C., Université de Lausanne, CH-1015 Lausanne-Dorigny, Switzerland.
Katholieke Universiteit Leuven, Instituut voor Aktuariele Wetenschappen, B-3000 Leuven, Belgium.
Universiteit van Amsterdam, Jodenbreestraat 23, NL-1011 NH Amsterdam, Netherlands.
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Abstract

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In the usual model of the collective risk theory, we are interested in the severity of ruin, as well as its probability. As a quantitative measure, we propose G(u, y), the probability that for given initial surplus u ruin will occur and that the deficit at the time of ruin will be less than y, and the corresponding density g(u, y). First a general answer in terms of the transform is obtained. Then, assuming that the claim amount distribution is a combination of exponential distributions, we determine g; here the roots of the equation that defines the adjustment coefficient play a central role. An explicit answer is also given in the case in which all claims are of constant size.

Keywords

Ruinseverity of ruin
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 17 , Issue 2 , November 1987 , pp. 151 - 163
Copyright
Copyright © International Actuarial Association 1987

References

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