马氏调制的跳扩散风险模型的破产概率

Ruin Probablities of Markov-modulated Jump-diffusion Risk Model

本文研究了一类带布朗运动扩散项的复合泊松风险模型,即跳扩散风险模型,利用谱负Levy过程的性质,得到了其破产概率的表达式.在此基础上,定义了马尔科夫环境过程,对在马尔可夫环境下的跳扩散风险模型进行了深入研究,给出了马氏调制的跳扩散风险模型的破产概率满足的积分微分方程,并用Laplace变换的方法进一步得到最终破产概率所满足的Volterra积分方程组.最后用两状态的马尔科夫环境过程,对模型的结论进行了算例说明.

The compound Poisson risk model perturbed by diffusion,which is so-called jump-diffusion risk model,is discussed and the expression of the ruin probability is given by the properties of spectrum negative Levy process.Furthermore,by introducing a Markovian environment process,the Markov-modulate jump-diffusion risk model is studied,whose integro-differential equations of the ultimate ruin probabilities are given.The Volterra integral equations for the ruin probabilities of this Markov-modulated jump-diffusion risk model are obtained by means of Laplace transform.In the end,two-state Markovian environment process is used as an example to explain the conclusion of the paper.