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Improved Analytical Bounds for Some Risk Quantities

Published online by Cambridge University Press:  29 August 2014

Werner Hürlimann
Werner Hürlimann*
Affiliation:
Allgemeine Mathematik, Paulstr. 9, Winterthur-Leben
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Abstract

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Simple analytical lower and upper bounds are obtained for stop-loss premiums and ruin probabilities of compound Poisson risks in case the mean, variance and range of the claim size distribution are known. They are based on stop-loss extremal distributions and improve the bounds derived earlier from dangerous extremal distributions. The special bounds obtained in case the relative variance of the claim size is unknown, but its maximal value is known, are related to other actuarial results.

Keywords

analytical boundsstop-lossruin probabilitystochastic orderingsrelative varianceatomic distributions
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 26 , Issue 2 , November 1996 , pp. 185 - 199
Copyright
Copyright © International Actuarial Association 1996

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