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

Gordon E. Willmot and Jae-Kyung Woo

ASTIN Bulletin, 2013, vol. 43, issue 2, 189-212

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.

Date: 2013
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