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On the Probability and Severity of Ruin

Gerber, Hans U. ; Goovaerts, Marc J. ; Kaas, Rob

In: ASTIN Bulletin, 1987, vol. 17, no. 2, p. 151-163

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    Title
    • On the Probability and Severity of Ruin
    Author
    • Gerber, Hans U.. Université de Lausanne
    • Goovaerts, Marc J.. K. U. Leuven and University of Amsterdam
    • Kaas, Rob. University of Amsterdam
    Document Type
    • Postprint
    OAI-PMH Identifier
    • oai:doc.rero.ch:299951
    Summary
    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