马氏调制费率的带干扰风险模型

孙歆; $2; 方世祖

马氏调制费率的带干扰风险模型

引用本文：孙歆，段誉，方世祖.马氏调制费率的带干扰风险模型[J].经济数学,2012,(1):100-105

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作者	单位
孙歆，段誉，方世祖	(1. 毕节学院数学系，贵州毕节551700；2. 广西大学数学与信息科学学院，广西南宁530004)

中文摘要:考虑了一类具有马氏调制的带干扰连续时间风险模型,得到了该模型下其条件Gerber-Shiu折现罚金函数所满足的积分方程,Laplace变换及渐近解.在两状态情形下,当索赔额的分布为有理数情况时得到了条件Gerber-Shiu折现罚金函数的具体表达式并给出了数值例子

中文关键词:马氏调制 Gerber-shiu折现罚金函数 Laplace变换

A Markov-Modulated Risk Model Perturbed by Diffusion

Abstract:This paper studied a Markov-modulated premium income risk model perturbed by diffusion under the condition of continuous time. The integral representations for the conditional Gerber-Shiu discounted penalty functions and the Laplace transforms of them were derived, and the asymptotic estimates for the conditional Gerber-Shiu discounted penalty functions were also derived. Under the two states model, when the claim size distribution is from the rational family,the explicit solution for the conditional Gerber-Shiu discounted penalty functions was derived. As an application,a number example was given.

keywords:Markov-modulated Gerber-Shiu discounted penalty function Laplace transform

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