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On the Probability and Severity of Ruin

Published online by Cambridge University Press:  29 August 2014

Hans U. Gerber ,
Marc J. Goovaerts  and
Rob Kaas
Hans U. Gerber*
Affiliation:
Université de Lausanne
Marc J. Goovaerts*
Affiliation:
K. U. Leuven and University of Amsterdam
Rob Kaas*
Affiliation:
University of Amsterdam
*
Ecole des H.E.C., Université de Lausanne, CH-1015 Lausanne-Dorigny, Switzerland.
Katholieke Universiteit Leuven, Instituut voor Aktuariele Wetenschappen, B-3000 Leuven, Belgium.
Universiteit van Amsterdam, Jodenbreestraat 23, NL-1011 NH Amsterdam, Netherlands.
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Abstract

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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

Ruinseverity of ruin
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 17 , Issue 2 , November 1987 , pp. 151 - 163
Copyright
Copyright © International Actuarial Association 1987

References

Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A. and Nesbitt, C. J. (1987) Actuarial Mathematics, Society of Actuaries.Google Scholar
Cramér, H. (1955) Collective risk theory — A survey of the theory from the point of view of the theory of stochastic processes. The Jubilee Volume of Skandia.Google Scholar
Dickson, D. C. M. and Gray, J. R. (1984) Exact solutions for ruin probability in the presence of an absorbing upper barrier. Scandinavian Actuarial Journal, 174–186.CrossRefGoogle Scholar
Feller, W. (1966) An Introduction to Probability Theory and its Applications vol. 2. Wiley.Google Scholar
Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vetterling, W. T. (1986) Numerical Recipes — The Art of Scientific Computing. Cambridge University Press, Cambridge.Google Scholar
Shiu, E. S. W. (1985) Convolution of Uniform Distribution. Technical Report, University of Manitoba.Google Scholar
Stoer, J. (1972) Einführung in die Numerische Mathematik I. Springer-Verlag, Berlin.CrossRefGoogle Scholar