带干扰的MAP风险过程的期望贴现惩罚函数  

Gerber-Shiu Function of MAP Risk Process Perturbed by Diffusion

作　　者：唐胜达[1] 秦永松[1] 

机构地区：[1]广西师范大学数学科学学院,广西桂林541004

出　　处：《广西师范大学学报（自然科学版）》2011年第3期23-27,共5页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(10971038);广西教育厅科研资助项目(201106LX067)

摘　　要：本文讨论了索赔到达过程为一般Markov点过程,即考虑索赔到达为MAP过程的一类带干扰的风险模型,给出了期望贴现惩罚函数的Laplace变换满足的积分-微分方程,对于Laplace变换为有理函数的索赔分布,采用差分变换方法,利用Dickson-Hipp算子,本文得到了期望贴现惩罚函数的简洁表达式。A risk model perturbed by diffusion is proposed in this paper.Claims arrival belongs to markovian arrival process（MAP）.The integro-differential equations satisfied by Laplace transform of the Gerber-Shiu functions and closed form of expression for the Gerber-Shiu functions are obtained through divided difference and Dickson-Hipp operator when the claim amount distribution is from the rational family.Finally,in order to illustrate the main results,a numerical example is provided.

关 键 词：风险过程 期望贴现惩罚函数 MAP过程 积分-微分方程 LAPLACE变换 

分 类 号：O211.9[理学—概率论与数理统计]