On the expected discounted penalty function for a risk model with dependence under a multi-layer dividend strategy

ABSTRACT

In this article, we consider a dependent risk model in the presence of a multi-laydividend strategy. We construct the dependence structure between the claim size and interclaim time by a Farlie–Gumbel–Morgenstern copula. A piecewise integro-differential equations for the expected discounted penalty function with boundary conditions are established. A renewal equation satisfied by the expected discounted penalty function is obtained via the translation operator. Then, we provide a recursive approach to derive the analytical solution of the expected discounted penalty function. Finally, a numerical example is presented to illustrate the solution procedure.

KEYWORDS:

• Compound Poisson risk model
• Dependence
• Expected discounted penalty function
• Farlie–Gumbel–Morgenstern copula
• Multi-layer dividend strategy

Mathematics Subject Clssification:

• 62P05
• 91B30

Funding

The research of the first author was supported by the Natural Science Foundation of China (Grant No. 11561047, 11201217), the Natural Science Foundation of JiangXi Province (Grant No. 20132BAB211010), and the STRP of JiangXi Province (Grant No. GJJ151101). The research of the second author was supported by the Natural Science Foundation of JiangXi Province (Grant No. 20142BAB211015), and the STRP of JiangXi Province (Grant No. GJJ151116).