A Class Discussion Of The Bivariate Risk Model

The classical insurance risk model and its expanded ones offer many mathematical models for describing single insurance risk management process. But with the development of business scale of the insurance company, it is unfeasible for a company to undertake the single risk management model.In this paper, the author present a new model in which the claim is the double risk management model perturbed by diffusion. In this new model, the claim access process is the integration of the compound Poisson process and the Erlang(2) process. The conditional expect theory is adopted to discuss the ultimate ruin probability.In the latter of the paper, the model is also expanded to the model which the two claim access process are correlated, and obtain the transformation of the ultimate ruin probability.The thesis is divided into three chapters according to contents:In Chapter 1, we consider the development of the risk theory and main result, the conclusion of the classical risk model.In Chapter 2, we present the classical risk model and some results of this model, such as the ruin probability and the discounted penalty satisfies a certain renewal equation and other results. We also present the Erlang(2) process and some results about the double insurance risk model that we will be used in the next chapter.In Chapter 3, we study a class of double risk model. Basic on the conclusion of the Erlang(2) risk model and the classical risk model, we use the method of the classical risk model, then we can get some results of the new risk model. We also give the prove that the model which never translated. Next we considered the risk model with constant interest force, perturbed by diffusion. In the last of the paper, we also consider the double insurance risk model with two claim access process are not independent, get some united ruin probabilities and up bounds.