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Methodology and Computing in Applied Probability

, Volume 13, Issue 3, pp 487–510 | Cite as

Constant Dividend Barrier in a Risk Model with a Generalized Farlie-Gumbel-Morgenstern Copula

  • Hélène Cossette
  • Etienne Marceau
  • Fouad Marri
Article

Abstract

In this paper, we consider the classical surplus process with a constant dividend barrier and a dependence structure between the claim amounts and the inter-claim times. We derive an integro-differential equation with boundary conditions. Its solution is expressed as the Gerber-Shiu discounted penalty function in the absence of a dividend barrier plus a linear combination of a finite number of linearly independent particular solutions to the associated homogeneous integro-differential equation. Finally, we obtain an explicit solution when the claim amounts are exponentially distributed and we investigate the effects of dependence on ruin quantities.

Keywords

Compound Poisson risk model Copula Generalized Farlie-Gumbel-Morgenstern copulas Constant dividend barrier Ruin theory Dependence models Gerber-Shiu discounted penalty function 

AMS 2000 Subject Classification

Primary 62P05; Secondary 60K05 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Hélène Cossette
    • 1
  • Etienne Marceau
    • 1
  • Fouad Marri
    • 1
  1. 1.École d’ActuariatUniversité LavalQuébecCanada

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