马氏调制费率的带干扰风险模型
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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5517002. 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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