Ruin Probabilities for Markov-Modulated Jump-Diffusion Risk Model

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.