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A Gaussian Exponential Approximation to Some Compound Poisson Distributions

Published online by Cambridge University Press:  17 April 2015

Werner Hürlimann
Werner Hürlimann*
Affiliation:
Winterthur Life and Pensions, Value and Risk Management, Postfach 300 CH-8401, Winterthur, Switzerland
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Abstract

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A three parameter Gaussian exponential approximation to some compound Poisson distributions is considered. It is constructed by specifying the reciprocal of the mean excess function as a linear affine function below some threshold and a positive constant above this threshold. As an analytical approximation to compound Poisson distributions, it is only feasible either for a limited range of the Poisson parameter or for higher coefficients of variation. A semiparametric determination of the unknown threshold parameter is proposed. The analysis of a real-life example from pension fund mathematics displays an improved quality of fit of the new model when compared with other simple good alternative approximations based on the zero gamma, translated gamma and zero translated gamma.

Keywords

Compound Poisson distributionGauss densityexponential densitymean excess functionstop-loss transformanalytical approximationthreshold parameter
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 33 , Issue 1 , May 2003 , pp. 41 - 55
Copyright
Copyright © ASTIN Bulletin 2003

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