The Study Of Ruin Probability Of Correlated Risk Model Pertured By Diffusion

Risk theory is general theory that risk managers or decision makers quantitatively analysis and forecast the risk, but the classical risk model and its extension model are to describe the risk of a single type of insurance. As the business scale of the insurance company is expanding, the classical risk model already exists serious limitations, and the research of more types of insurance is more close to the real, especially correlated risk model have more research value.Firstly, we introduce the basic theory of classical risk theory. And then, we will deeply summarize and study two classic methods of risk theory that are martingale theorem and renewal theorem. At the same time, in order to describe the operating conditions of insurance company more accurately, we extend and study the classical risk model by using the theory of stochastic analysis, stochastic process, martingale theorem and so on. It is more satisfied with the actual situation while the insurance company has more business. This paper mainly studies the two kinds of correlated risk model. On the basis of classical risk model, we suppose the counting process are correlated. While the correlated part is Poisson process, we analyses the nature of the profit process, then we get the explicit expression and the upper bound of ruin probability about the corresponding risk model by using the way of martingale analytic technique. While the correlated part is Erlang(2) process; we constructe a delayed renewal process, then to derive the integral-differential equations satisfied by the survival probabilities under the assumed model and the upper bound of the ruin probabilities by using the way of stochastic process.Finally, this article obtains different expression form of ruin probability under different risk model and then gives the prospect of this paper.