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Communications in Statistics - Theory and Methods Volume 46, 2017 - Issue 4
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Original Articles

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

Jie-Hua XieSchool of Economics and Trade, Nanchang Institute of Technology, Nanchang, P.R. China
&
Wei ZouSchool of Science, Nanchang Institute of Technology, Nanchang, P.R. ChinaCorrespondence[email protected]
Pages 1898-1915 | Received 03 Nov 2014, Accepted 10 Mar 2015, Published online: 16 Mar 2016
 
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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.

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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).

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