On the Probability and Severity of Ruin

Hans U. Gerber, Marc Goovaerts and Rob Kaas

ASTIN Bulletin, 1987, vol. 17, issue 2, 151-163

Abstract: 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.

Date: 1987
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