带干扰的MAP风险过程的期望贴现惩罚函数

广西师范大学学报（自然科学版） ›› 2011, Vol. 29 ›› Issue (3): 23-27.

带干扰的MAP风险过程的期望贴现惩罚函数

唐胜达, 秦永松

广西师范大学数学科学学院,广西桂林541004

收稿日期:2011-04-29 出版日期:2011-08-20 发布日期:2018-12-03
通讯作者: 秦永松(1964—),男,湖北鄂州人,广西师范大学教授,博士。E-mail:ysqin@mailbox.gxnu.edu.cn
基金资助:
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)

Gerber-Shiu Function of MAP Risk Process Perturbedby Diffusion

TANG Sheng-da, QIN Yong-song

College of Mathematical Science,Guangxi Normal University,Guilin Guangxi 541004,China

Received:2011-04-29 Online:2011-08-20 Published:2018-12-03

摘要/Abstract

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。

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

Abstract: 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.

Key words: risk theory, Gerber-Shiu function, MAP, Integro-differential equation, Laplace transform

中图分类号:

O211.9

唐胜达, 秦永松. 带干扰的MAP风险过程的期望贴现惩罚函数[J]. 广西师范大学学报（自然科学版）, 2011, 29(3): 23-27.

TANG Sheng-da, QIN Yong-song. Gerber-Shiu Function of MAP Risk Process Perturbedby Diffusion[J]. Journal of Guangxi Normal University(Natural Science Edition), 2011, 29(3): 23-27.

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