带扰动的广义Erlang(n)风险过程最大亏损问题研究  

The Maximum Severity of Ruin in a Generalized Erlang(n) Risk Process Perturbed by Diffusion

作　　者：王健[1] 王传玉[1] 周金乐 

机构地区：[1]安徽工程大学数理学院,安徽芜湖241000

出　　处：《盐城工学院学报（自然科学版）》2015年第1期9-15,共7页Journal of Yancheng Institute of Technology:Natural Science Edition

基　　金：国家自然科学基金项目(61203139);安徽省重点教研项目(2012jyxm277)

摘　　要：运用Laplace变换,研究了带扰动的广义Erlang(n)风险模型最大亏损的分布,求得满足生存概率的一个积分-微分方程的解。它的解可以表示为2n阶线性独立特解的一个线性组合,当n=2时,得到最大亏损分布的精确表达式,再通过一个实例来说明该研究结果。In this paper,we discuss the distribution of the maximum severity of ruin from the time of ruin until the time that the surplus returns to level 0 in a generalized Erlang（n） risk process perturbed by diffusion.Then,we solve an integro-differential equation that is satisfied by the survival probability by the way of Laplace transform.Its solution can be expressed as a linear combination of 2n linearly independent particular solutions of the integro-differential equation.When n = 2,the maximum severity of ruin can be expressed explicitly in terms of the non-ruin probability.Finally,the research results of this paper are illustrated through an instance.

关 键 词：带扰动的广义Erlang(n)风险模型 广义Erlang(n)索赔间隔 积分-微分方程 最大亏损 

分 类 号：O211.9[理学—概率论与数理统计]