Markov链利率风险模型的破产问题

Ruin Problems with a Markov Chain Interest Model

基于Markov链具有的将来利率与过去利率的独立性,利用全概率公式与递推方法,探讨了破产前最大盈余和首达某一水平x的情况。首先得到破产前最大盈余的递推方程和积分方程,然后利用这种思路得到首达某一水平x的递推方程和积分方程,最后进一步完善了离散时间风险模型的结论。

This paper studies a discrete time risk model with a Markov chain interest. Since a Markov chain interest model reflects the independence of future rates and present rates, the maximum surplus distribution before rain and the time when the surplus process reaches a given level x for the first time are discussed with the help of the full probability formula and the recursive method. Recursive and integral equations of the maximum surplus distribution before ruin are given, and then recursive and integral equations of the time that the surplus process reaches a given level for the first time are obtained. The conclusions of discrete time risk model are further improved.