Dual Insurance Risk Model With Interference Discussions And Two-dimensional Risk Model Results

This paper discusses the problem of ruin probability in risk theory. The paper falls into three sections.First of all, we make a survey on the ruin theory and introduce the development of the ruin theory. The classic Lundberg risk model and related conclusions are introduced and the Gerber's martingale method and Feller's renewal argument, which are used to get the ruin probability of risk models, are also discussed. Then the trend of ruin theory in recent years is briefly recommended.Section two describes in detail a risk model with claim frequency which is a Cox process. The model is generalized from the classic risk model. Then the exact expression of ruin probability and Lundberg inequality of the new risk model is explained. Furthermore, several special cases of this risk model are discussed.Section three is focused on two dimensional risk models. We present three definitions of ruin probability under the case of two dimensions. After transferring the two dimensional case into univariate case, we get the explicit function of ruin probability with the results of section two and the third type is presented as an example.