Analysis of ruin measures for the classical compound Poisson risk model with dependence

Héléne Cossette, Etienne Marceau and Fouad Marri

Scandinavian Actuarial Journal, 2010, vol. 2010, issue 3, 221-245

Abstract: In this paper, we consider an extension to the classical compound Poisson risk model. Historically, it has been assumed that the claim amounts and claim inter-arrival times are independent. In this contribution, a dependence structure between the claim amount and the interclaim time is introduced through a Farlie–Gumbel–Morgenstern copula. In this framework, we derive the integro-differential equation and the Laplace transform (LT) of the Gerber–Shiu discounted penalty function. An explicit expression for the LT of the discounted value of a general function of the deficit at ruin is obtained for claim amounts having an exponential distribution.

Date: 2010
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DOI: 10.1080/03461230903211992

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