马氏调节风险模型下的有限时间破产问题

Some Finite Time Ruin Problems in Markov-Modulated Risk Model

本文主要研究马氏调节模型中有限时间内的破产变量的分布,给出了有限时间内索赔次数的分布律、总索赔金额的分布函数,且采用了离散近似的方法,显示近似方法的结果与精确的概率密度函数非常接近.此外,使用分解概率密度函数的方法,求出破产时间和破产时赤字的联合分布的具体表达式.

This paper studies the distribution of finite-time ruin quantities.It gives the probability mass function of finite time number of claims,and find the distribution function of aggregate claims by using discretise method and compared with exact distribution function,which shows that the approximation works very well.In addition,by applying decomposition for density function,it gives the explicit expression for joint density of ruin time and deficit at ruin.