Bankruptcy Probability Of The Risk Model With Interference

Classical ruin theory assumes that the surplus in an insurance company has stationary and independent increments.However,because of the increasing complexity of insurance and reinsurance products,it can't describe the realistic process well.Because the estimate of ruin probability is important to stability of insurance company,so it is necessary to construct models which can describe realism well.The classical risk model is generalized to a new risk model by many people. This text study the ruin probability based on Zhang(2005)and Gaoshan(2005).Chapter Ⅰ is preface. I introduce some knowledge of ruin theory, contenting the grounds of ruin theory,methods,main conclusion in the ruin theory.Chapter Ⅱ analyzes a continuous time risk model with a linear model used to model the claim process.At the same time ,we consider the risk model perturbed by diffu-sion.We introduce stochastic process describing premium process,using Doob's stopping time theorem and martingale method to obtain expressions for the ruin probability as well as Lundberg inequality for the ruin probability for an infinite time hori-zon.Furthermore,by the concrete example,the relationship between the ruin probability ,the initial capital,the premium amounts and the claim amounts is discussed.Chapter Ⅲ introduce a risk model based on a Cox model used to model the claim process and premium process,where the arrival of the claims follows a p-thinning process of the arrival process. .Furthermore/we consider a diffusion in the risk model.For this kind of risk model,we obtain the upper bound of the eventual ruin probability.