On the analysis of time dependent claims in a class of birth process claim count models |
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| Affiliation: | 1. School of Risk and Actuarial Studies, University of New South Wales, Sydney, Australia;2. CEPAR, Australia;1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA;2. Department of Mathematics, York University, Toronto, Ontario, Canada M3J 1P3;1. University of Technology, Sydney, The Finance Discipline Group, UTS Business School, PO Box 123, Broadway, NSW, 2007, Australia;2. Auckland University of Technology, Department of Finance, Private Bag 92006, 1142 Auckland, New Zealand;3. Università degli Studi di Padova, Dipartimento di Matematica, Via Trieste 63, Padova, Italy;4. Devinci Finance Lab, Pôle Universitaire Léonard de Vinci, 92916 Paris La Défense Cedex, France;5. Quanta Finanza srl, Via Cappuccina 40, Mestre (Venezia), Italy;1. Department of Mathematics, Michigan State University, East Lansing, MI 48824, United States;2. Towers Watson, Hartford office, University of Connecticut, Storrs, CT 06269-3009, United States;3. Department of Mathematics, University of Connecticut, Storrs, CT 06269-3009, United States;1. School of Sciences, Hebei University of Technology, PR China;2. Department of Statistics and Actuarial Science, Simon Fraser University, Canada |
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| 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. |
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| Keywords: | Transition probabilities Inflation IBNR Contagion Mixed Poisson Compound distribution Random sum |
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