The Study Of The Ruin Probabilities For Risk Processes With Non-Stationary And Heavy-Tailed Claims

Risk is the core of risk theory. The essence of the risk is the uncertain and random loss. The classical theory studies the small claims’ case of bankruptcy theory under the stationary independent assumptions. It is not suitable for the strong randomness and large claims risk, such as fire, storm and flood risks, etc. The strong constraint of the classical theory is that it needs the exist of adjustment coefficient. So the subexponential distribution is a new mathematical tool to study the bankruptcy theory of large claims’case. The stationary assumptions in the classical risk model is too harsh, it does not conform to strong randomness of claim with the insurance company’s actual operation. So it is particularly necessary to study the risk model of the non-stationary arrival process.This paper sets from the classical risk model. It expands the risk processes and the distribution of the claim. First, it studies the non-stationary arrived under the heavy-tailed claims. It uses negative dependency properties, heavy-tailed distribution and the method of large deviation principle, it obtains the expression of the model of infinite time and finite time ruin probability and precise large deviation. Then the dual risk model of the dependent claim is studied. Considering the main and the auxiliary claim which occurred in the process of risk, both of them are obeyed subexponential distribution. It obtains the expression of the finite and the infinite levels of progressive of the ruin probability and the total tail, using the properties of heavy-tailed distribution and large deviation principle.In this paper, the risk model is set up under the condition of claim distribution which is heavy-tailed distribution and claim number process which is non-stationary. It improves and perfects the risk theory model, and it is more realistic. The theoretical tool is provided for the insurance industry to assess and predict the risk. So the model in this paper has certain practical application value.Finally, it makes a conclusion to the result, and it gives a prospect to people of this paper.