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Document Details : Title: On the Probability and Severity of Ruin Author(s): GERBER, Hans U. , GOOVAERTS, Marc J. , KAAS, Rob Journal: ASTIN Bulletin Volume: 17 Issue: 2 Date: November 1987 Pages: 151-163 DOI: 10.2143/AST.17.2.2014970 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 transform is obtained. Then, assuming that the claim amount distribution is a combination of 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. |
