Ruin Probability For A Markov-modulated Risk Model

Ruin theory is the core of the risk theory,which can be tracked back to the doctoral dissertation published by Lundberg,F.at1903. Because the assumption of the classical ruin model is too strong, which differed greatly with the realities,so its practical is not well. So far, the study about the theory of bankruptcy, in terms of vertical or lateral direction, is becoming more expanded.At the same time,people began to discuss more complex problems about ruin model more close to the reality.The general modifications include:add a diffusion pro-cess to the classical risk process,change the claim patern,add a dividend barrier or use a Markov Chain to control the parameter,and so on.The author summarizes some works of people in this area,and will systematically make improvements on the classical ruin model to make it more realistic and easy to practical use.In this paper,the model about ruin probability isThere are mainly four points to improve the classical ruin model:(1),the premium rate which was a constant in the classical model is a function for the current.(2),the interclaim arrivals and the claim sizes are no longer independent,but exist a dependence structure.(3),the paper will add a diffusion process(a disturbance factor).(4),here,we no longer assume the claim number process is a poisson process,but a cox process,and its intensity process is a homogenous,irreducible,and recurrent Markov processes with finite state space.Work in this area has many follow-up parts. Next, I will extend the research on the ruin probability of promotion to the expected discounted penalty function.