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

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  • Héléne Cossette
  • Etienne Marceau
  • Fouad Marri

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.

Suggested Citation

  • Héléne Cossette & Etienne Marceau & Fouad Marri, 2010. "Analysis of ruin measures for the classical compound Poisson risk model with dependence," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2010(3), pages 221-245.
  • Handle: RePEc:taf:sactxx:v:2010:y:2010:i:3:p:221-245
    DOI: 10.1080/03461230903211992
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