Double Insurance Ruin Probability With Interference

Risk theory is an important branch of modem mathematics, which is mainly applied in finance, insurance, securities investment and the risk management. Nowadays, the collective risk theory is one of the most intriguing fields both actuarial and mathematical science. There are many researches on one-type risk model. It is necessary to build multi-type risk model for extending of managing scales. The paper mainly studies two-type risk model with random disturbing item.Firstly, it introduces the development of the ruin theory, the classical risk model and related conclusions, it also summarizes the classical risk model and its generalizations. Secondly, we introduce the basic knowledge of risk theory and the principium of ruin theory. Thirdly, on the basis of the classical model, it is generalized to two-type risk model with random disturbing item, in which the income of premium is not a constant in unit time, it is a variable, and the processes of premium income is Poisson process. We deduce the expression of ruin probability of the risk model and the Lundberg inequality. Also we obtain the upper and the lower bound of the adjust coefficient. At last, base on the third chapter, the arrival processes of claims are generalized to generalized Poisson process and Cox process, and the arriving times of claims are dependent, then the Lundberg inequality is given. When we substitute the Cox process for Erlang (2) process, we gain the similar results as the classical model.