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The maximum surplus before ruin for dependent risk models through Farlie–Gumbel–Morgenstern copula

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  • Wuyuan Jiang
  • Zhaojun Yang

Abstract

We extend the classical compound Poisson risk model to consider the distribution of the maximum surplus before ruin where the claim sizes depend on inter-claim times via the Farlie–Gumbel–Morgenstern copula. We derive an integro-differential equation with certain boundary conditions for this distribution, of which the Laplace transform is provided. We obtain the renewal equation and explicit expressions for this distribution are derived when the claim amounts are exponentially distributed. Finally, we present numerical examples.

Suggested Citation

  • Wuyuan Jiang & Zhaojun Yang, 2016. "The maximum surplus before ruin for dependent risk models through Farlie–Gumbel–Morgenstern copula," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2016(5), pages 385-397, May.
    • Handle: RePEc:taf:sactxx:v:2016:y:2016:i:5:p:385-397
    DOI: 10.1080/03461238.2014.936972
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