On the Probability and Severity of Ruin

Abstract

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.