Year: 1987
Type: article
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.
Source: Astin Bulletin
Authors: Hans U. Gerber, Marc J. Goovaerts, Rob Kaas
Institutions: University of Lausanne, University of Amsterdam, KU Leuven
Language: English
Topic: Probability and Risk Models
Field: Decision Sciences
Domain: Social Sciences
Open Access status: bronze
OpenAlex ID: W2011748898