On the Probability and Severity of Ruin
Open Access
- 1 November 1987
- journal article
- Published by Cambridge University Press (CUP) in ASTIN Bulletin
- Vol. 17 (2) , 151-163
- https://doi.org/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 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
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