The Research On Double Line Risk Model With Interference Under Different Factors

Risk theory is a hot topic in the present actuarial science and mathematics research. As an important component of application mathematics in modern, risk theory is that the operator or the decision-maker assess risk and predict risk. The main research of risk theory is stochastic risk models in insurance matters and the security from a quantitative point of view of insurance company.Bankruptcy theory of insurance risk theory is the important issue. Ruin probability research of risk models in bankruptcy theory is very active. The research provides a very useful means of early risk warning for decision-makers of insurance company, so their study has important theoretical and practical significance. The classical compound Poisson risk model is a kind of most basic model, but this kind of model also has certain limitation in certain actual problem's application, therefore we carry on the promotion in the classical risk model's foundation from two aspects. The first, conducts the research to the Poisson-Geometric risk model. That is we consider ruin probability for a Poisson—Geometric risk model of double line with Interference under stochastic interest. The second, we consider ruin probability for a compound generalized homogeneous Poisson risk model of double line with interference under stochastic interest. The thesis includes four chapters:The first chapter:Introduces the evolutional course and actuality of risk model, expounded the direction, content and significance of this thesis.The second chapter:Imports the classical risk model and gives a definition of risk model of double line with interference under stochastic interest.The third chapter:This paper is meant to study a risk model of double line with stochastic interest and interference is established. In case of the claim process following a Poisson—Geometric process, the final ruin probability is derived.The forth chapter:the classic compound Poisson risk model is generalized and a compound generalized homogeneous Poisson ruin model of double line is set up. In the risk model, the stochastic interest and Brown motion interference are considered. By analyzing the ruin model, adjustment coefficient equation is set up and the upper bound for adjustment coefficient is estimated. The ruin probabilityΨ(u) is derived.