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SOME DISTRIBUTIONAL PROPERTIES OF A CLASS OF COUNTING DISTRIBUTIONS WITH CLAIMS ANALYSIS APPLICATIONS

Published online by Cambridge University Press:  18 June 2013

Gordon E. Willmot  and
Jae-Kyung Woo
Gordon E. Willmot
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada E-Mail: [email protected]
Jae-Kyung Woo*
Affiliation:
Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong
*
E-Mail: [email protected]
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Abstract

We discuss a class of counting distributions motivated by a problem in discrete surplus analysis, and special cases of which have applications in stop-loss, discrete Tail value at risk (TVaR) and claim count modelling. Explicit formulas are developed, and the mixed Poisson case is considered in some detail. Simplifications occur for some underlying negative binomial and related models, where in some cases compound geometric distributions arise naturally. Applications to claim count and aggregate claims models are then given.

Keywords

Mixed Poissoncompound geometricmixed geometricnegative binomiallogarithmic seriescompletely monotoneshifting and truncationDickson–HippGerber–Shiustop-lossequilibrium distributionPanjer recursion
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 43 , Issue 2 , May 2013 , pp. 189 - 212
Copyright
Copyright © ASTIN Bulletin 2013 

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