The Research About Dividend And Ruin Problems Of The Generalized Discrete Time Risk Model

This paper introduces the discrete time risk model:we assume that the premiums and claims in every time are all random variables which independent and identically dis-tributed. And the collection of premiums occurs in the beginning of each time period, the claim occurs in the end of each time period. At first, we introduce the classical risk model, then we import the interest factor and the dividend strategy factor basic in this model, The generalized models are the constant interest risk model and the dividend strategy model(includes the dividend barrier strategy model and the double thresholds strategy model). In each risk model, we discuss ruin problems.and get the expressions about ruin probability, distribution of surplus immediately before ruin, distribution of deficit at ruin, the Gerber-Shiu discounted penalty function and so on; Discuss the div-idend problems about the company, we get the expressions about the expectation of discounted dividends before ruin and the kth moment of expected discounted dividend before ruin. Among the expectation of discounted dividends, we study three kinds of sit-uation:the dividend barrier strategy without interest; the dividend barrier strategy with constant interest; the double thresholds strategy without interest. Then we introduce the definition of the contraction mapping principle and the theory of the fixed point, we use a new method-iterative evaluation method to calculate the approximate amount. At last, we random simulate the dividend and use the formula we contained to calculate the expected discounted dividend, receive another approximation, then systematic analysis the two sets of data.