Supper Bounds For Ruin Probabilities In Two Varieties Of Dependent Risk Models

Business solvency is the " lifeline " of insurance company, and one of the most important indexes to weigh it is the ruin probability . So the ruin probability plays an important role in actuarial science. Ruin probability of the insurance risk model has been extensively studied. Because of the increasing complexity of insurance and reinsurance products, comparing with the classical risk model, it is more realistic to consider dependent risk models with rates of interest.In this paper, we consider two varieties of discrete-time insurance risk models. In Chapter 2, two moving average risk models are introduced to model the surplus process, and the probabilities of ruin are examined in models with a constant interest force. Exponential bounds for ruin probabilities of an infinite time horizon are derived by martingale method. And we compare them with some relative existing research results of other scholars. In fact, the models we consider in Chapter 1 are based on Gerber(1982) and Yang(1998) respectively , Theorem 1 of Gerber(1982) and Theorem 3.1 of Yang(1998) are special cases of our results correspondingly. In Chapter 3, generalizing the models of Cai(2002), we use two autoregressive moving-average models to model the premiums and rates of interest respectively. And for the sake of argument , the claims are assumed to be independent. In the models the effects of time of payments and interest on the surplus process and on the ruin probability can be included. Integral equations and generalized Lundberg inequalities for the ruin probabilities are derived by a renewal recursive technique. The results in Cai(2002) become special cases of ours. In the end of Chapter 3 we give several numerical examples to illustrate the accuracy of the upper bounds and point out the influence on the ruin probabilities caused by parameters' variations.The risk models introduced in this paper are extensive to a certain extent. And some existing research results of other scholars can be considered as special cases of ours. We hope those generalized results are helpful to the scientific management of insurance company .