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Calculating Ruin Probabilities via Product Integration

Published online by Cambridge University Press:  29 August 2014

Colin M. Ramsay  and
Miguel A. Usabel
Colin M. Ramsay
Affiliation:
Actuarial Science Program, University of Nebraska-Lincoln, Lincoln NE 68588-0426, USA
Miguel A. Usabel
Affiliation:
Dto. Economia Financiera y Actuarial, UCM Campus de Somosaguas, Ftad. CC Economicas, Madrid, Spain
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Abstract

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When claims in the compound Poisson risk model are from a heavy-tailed distribution (such as the Pareto or the lognormal), traditional techniques used to compute the probability of ultimate ruin converge slowly to desired probabilities. Thus, faster and more accurate methods are needed. Product integration can be used in such situations to yield fast and accurate estimates of ruin probabilities because it uses quadrature weights that are suited to the underlying distribution. Tables of ruin probabilities for the Pareto and lognormal distributions are provided.

Keywords

Integral equationconvergenceheavy-tailed distributions
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 27 , Issue 2 , November 1997 , pp. 263 - 271
Copyright
Copyright © International Actuarial Association 1997

References

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