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The Risk Process with Dependence Based on FGM Copula under A Multi-Layer Dividend Strategy

Yang Long   

  1. School of Mathematics and Statistics, Guangxi Normal University, Guilin 541004
  • Received:2014-03-14 Revised:2015-02-24 Online:2015-10-25 Published:2015-10-25

Abstract:

In this paper, we consider an extension to the classical compound Poisson risk model under a multi-layer dividend strategy, in which the claim size and inter-claim time are dependent. We assume that the dependence structure between the claim size and the inter-claim time is based on a Farlie-Gumbel-Morgenstern copula. Some piecewise integro-differential equations with certain boundary conditions for the Gerber-Shiu function are derived. Then, applying these results, some defective renewal equations for the Gerber-Shiu function are obtained and explicit expressions are solved. Finally, to illustrate the solution procedure, explicit expressions for the ruin probability are given for exponential claim size.

Key words: Dependence structure, Multi-layer dividend strategy, Farlie-Gumbel-Morgenstern copula, Gerber-Shiu function, Defective renewal equation

CLC Number: 

  • O211.4
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