基于Coxian-2的相依风险模型的Gerber-Shiu惩罚函数  

Gerber-Shiu penalty function in a dependent risk model based on Coxian-2 distribution

作　　者：包振华[1] 李凤娟 BAO Zhenhua;LI Fengjuan(School of Mathematics,Liaoning Normal University,Dalian 116029,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2023年第3期307-312,共6页Journal of Liaoning Normal University:Natural Science Edition

基　　金：教育部人文社会科学研究一般项目(20YJA910001)。

摘　　要：考虑一类具有相依结构的风险过程,索赔额与索赔间隔时间之间的相依关系由FGM联结函数确定,而索赔间隔时间服从Coxian-2分布.首先研究了广义Lundberg方程根分布的情况,然后得到了Gerber-Shiu惩罚函数满足的微积分方程、拉普拉斯变换以及瑕疵更新方程.最后,在指数索赔的条件下获得破产概率的解析表达式并做数值分析.We consider a class of risk process with dependent structure,in which the claim sizes and interclaim times are related through FGM copula and the interclaim times follow the Coxian-2 distribution.Firstly,the roots of the generalized Lundberg equation is investigated.Then,the integro-differential equation,Laplace transform and defective renewal equation satisfied by the Gerber-Shiu penalty function are obtained.Finally,the explicit expressions for the ruin probability are given under exponential claim sizes and a numerical example is provided.

关 键 词：Gerber-Shiu惩罚函数 拉普拉斯变换 瑕疵更新方程 破产概率 

分 类 号：O211.67[理学—概率论与数理统计]