Study On The Ruin Problems And Dividend Related Issues Of A Class Of Discrete Time Risk Modles

As an important part of insurance actuarial,risk theory is the basic theory of quantitative analysis and risk prediction.In risk modles,the ruin probability and dividend problems is the focus of the study,these theories laid the foundations for the insurance companies in the study of new insurance,to determine premium rate and dividend policy,the initial reserve and the ratio of insurance and other issues.The problem of determining the dividend strategy and maximizing the value of the dividend under the strategy is a very concerned problem in the theoretical research.In this paper,we first discusse the problem of the dividend strategy of the discrete time risk model,and point out the optimal dividend strategy under certain conditions.And then we study the ruin and dividend problem of discrete time risk model with the barrier dividend strategy: integral equation of the ruin probability and the duration of the ruin are obtained by using the Gerber-Shiu function and the joint distribution function of the surplus immediately before ruin and the deficit after ruin;by recursive method we get the integral equation of expected discounted dividends,and the value of discounted dividends is given under some kind of special case and numerical examples are illustrated;from the time perspective,distribution function of the time to dividends is also studied in this paper.