On the analysis of time dependent claims in a class of birth process claim count models

David Landriault, Gordon E. Willmot and Di Xu

Insurance: Mathematics and Economics, 2014, vol. 58, issue C, 168-173

Abstract: An integral representation is derived for the sum of all claims over a finite interval when the claim value depends upon its incurral time. These time dependent claims, which generalize the usual compound model for aggregate claims, have insurance applications involving models for inflation and payment delays. The number of claims process is assumed to be a (possibly delayed) nonhomogeneous birth process, which includes the Poisson process, contagion models, and the mixed Poisson process, as special cases. Known simplified compound representations in these special cases are easily generalized to the conditional case, given the number of claims at the beginning of the interval. Applications to the case involving “two stages” are also considered.

Keywords: Transition probabilities; Inflation; IBNR; Contagion; Mixed Poisson; Compound distribution; Random sum (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:58:y:2014:i:c:p:168-173

DOI: 10.1016/j.insmatheco.2014.07.001

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