Markov随机环境过程驱动的风险过程

广西师范大学学报（自然科学版） ›› 2012, Vol. 30 ›› Issue (1): 35-39.

Markov随机环境过程驱动的风险过程

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:2011-10-08 出版日期:2012-01-20 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)

Risk Process Driven by Markovian Environment Process

TANG Sheng-da, QIN Yong-song

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

Received:2011-10-08 Online:2012-01-20 Published:2018-12-03

摘要/Abstract

摘要： 本文讨论由Markov环境过程驱动的风险过程,给出了期望贴现惩罚函数的Laplace变换的表达式,利用一般Lundberg基本方程,得到了期望贴现惩罚函数的简洁表达式,并推得了给定初始环境状态,初始资金为0时破产前瞬间盈余、破产赤字的贴现联合密度及其边缘密度。同时,本文也给出了破产时间、破产前瞬间盈余以及破产时赤字的矩的计算方法。

关键词: 风险过程, 期望贴现惩罚函数, Lundberg基本方程, 随机环境

Abstract: In this paper,a risk model driven by Markovian environment process that affects both the claim sizes and rates is described.The expression of Laplace transform of the Gerber-Shiu function is obtained.By means ofthe general Lundberg fundamental equation,the explicit expressions for the Gerber-Shiu functions with zero initial capital,the given state of environment,the discounted joint density functions and the density marginal density of the surplus prior to and after ruin are derived,respectively.Meanwhile,the methods to compute the arbitrary moments of the time to ruin,surplus before ruin and the deficit at ruin are also given.

Key words: risk process, Gerber-Shiu function, general Lundbergfundamental equation, Markovian environment

中图分类号:

O211.9

唐胜达, 秦永松. Markov随机环境过程驱动的风险过程[J]. 广西师范大学学报（自然科学版）, 2012, 30(1): 35-39.

TANG Sheng-da, QIN Yong-song. Risk Process Driven by Markovian Environment Process[J]. Journal of Guangxi Normal University(Natural Science Edition), 2012, 30(1): 35-39.

参考文献

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