多层分红策略下以FGM Copula为相依结构的风险模型

数学物理学报

多层分红策略下以FGM Copula为相依结构的风险模型

杨龙

广西省桂林市广西师范大学数学与统计学院桂林 541004

收稿日期:2014-03-14 修回日期:2015-02-24 出版日期:2015-10-25 发布日期:2015-10-25
作者简介:杨龙,yanglong1773@126.com

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

Yang Long

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

摘要/Abstract

摘要：

该文考虑了多层分红策略下相依的风险模型,用Farlie-Gumbel-Morgenstern(FGM) copula定义了索赔间隔时间和索赔额之间的相依结构,研究了Gerber-Shiu期望折扣罚金函数,导出了其所满足的积分微分方程和瑕疵更新方程,并给出了它们的解析解.最后,以索赔额分布服从指数分布为例,给出了破产概率所满足的具体解.

关键词: FGM copula, 相依结构, Gerber-Shiu函数, 多段分红策略, 瑕疵更新方程

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

中图分类号:

O211.4

杨龙. 多层分红策略下以FGM Copula为相依结构的风险模型[J]. 数学物理学报, 2015, 35(5): 1004-1017.

Yang Long. The Risk Process with Dependence Based on FGM Copula under A Multi-Layer Dividend Strategy[J]. Acta mathematica scientia,Series A, 2015, 35(5): 1004-1017.

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