Markov链利率离散时间比例再保险模型的破产问题

Ruin Problems for a Discrete Time Proportional Reinsurance Mode with Markov Chain Interest Rate

本文考虑了一类保费和理赔额均为相互独立随机变量,且利率为Markov链的离散时间比例再保险风险模型.利用递归更新技巧,得到了破产前盈余和破产后赤字的联合分布所满足的微积分方程,作为推论给出了保险公司最感兴趣的破产前盈余分布,破产后赤字的分布以及破产概率所满足的微积分方程.

In this paper,we study a discrete time proportional reinsurance risk mode under the assumption that the interest rates have Markov chain. By using the recursive method,the integro-differential equation for the distribution of the surplus just before ruin,the distribution of the surplus immediately after ruin,the joint distribution of the surplus immediately before and after ruin are derived. Moreover,as a corollary,the integral equations for the ruin probability are also derived.