Research On Bankruptcy Probabilities And Large Deviation Of Some Kinds Of Risk Models

This dissertation is based on the classical risk model. But we modify it with some kinds of methods according to reality's demand. At the same time, we consider the difference of heavy-tailed and light-tailed and get some conclusions about ruin probabilitie and large deviations.In chapter 2, we build the double Poisson risk model and get the conclusion on its large deviation in class C. Moreover, we introduce a smaller heavy-tailed class (class GERV). Then we get the same conclusion of large deviation and some correlative conclusions, too.In chapter 3, at first, we introduce the concept of generalized homogeneous Poisson process. In the last, we get its final ruin probabilities and Lundberg inequality by martingale method. In addition, we consider the situation that the numbers of claims and policies are non-homogeneous Poisson process and get a weak upper bound inequality of its probability.In chapter 4, we introduce the ordinary renewal risk model firstly. Then we change it to compound renewal risk model. At last, we get a equivalence relation of its probability..