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Approximations of Ruin Probability by Di-Atomic or Di-Exponential Claims

Published online by Cambridge University Press:  29 August 2014

Joshua Babier  and
Beda Chan
Joshua Babier*
Affiliation:
University of Toronto, Canada
Beda Chan*
Affiliation:
University of Toronto, Canada
*
Department of Statistics, 100 St George Street, University of Toronto, Toronto, Ontario, CanadaM5S 1A1.
Department of Statistics, 100 St George Street, University of Toronto, Toronto, Ontario, CanadaM5S 1A1.
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Abstract

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The sensitivity of the ruin probability depending on the claim size distribution has been the topic of several discussion papers in recent ASTIN Bulletins. This discussion was initiated by a question raised by Schmitter at the ASTIN Colloquium 1990 and attempts to make further contributions to this problem. We find the necessary and sufficient conditions for fitting three given moments by diatomic and diexponential distributions. We consider three examples drawn from fire (large spread), individual life (medium spread) and group life (small spread) insurance data, fit them with diatomics and diexponentials whenever the necessary and sufficient conditions are met, and compute the ruin probabilities using well known formulas for discrete and for combination of exponentials claim amounts. We then compare our approximations with the exact values that appeared in the literature. Finally we propose using diatomic and diexponential claim distributions as tools to study the Schmitter problem.

Keywords

Ruin probabilitydiatomic distributiondiexponential distribution
Type
Discussion Papers
Information
ASTIN Bulletin: The Journal of the IAA , Volume 22 , Issue 2 , November 1992 , pp. 235 - 246
Copyright
Copyright © International Actuarial Association 1992

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