Asymptotic Estimation And Uniform Estimation For The Ruin Probabilities In A Discrete Time Risk Model

Along with the development of the insurance industry, risk theory has been nearly a hundred years of history, it has formed a systematic theoretical system, at present the risk theory has extensive research prospect.With the continuous development of risk theory, many risk models used to study ruin probability emerged in which discrete time risk model is one of the most typical model. In this article we research discrete time risk model too, we primarily concern about ruin problem when the preliminary reserve of insurance company and collect premiums added up is still not enough to pay and has no funds of an insurance company to make other investment. This model considers the premium rate factors, and studies ruin probabilities under the assumptions that the individual net losses are bivariate upper-tail independent, identically distributed random variables having a common distribution in the class D∩L. We use two-side bounds method and Bonferroni inequality to prove the asymptotic estimation for finite time ruin probability, then we also use two-side bounds method to get the asymptotic estimation for infinite time ultimate ruin probability about discrete time risk model.Finally, in this article we make further researches on discrete time risk model and we use two-side bounds method to get the uniform estimation for finite time ruin probability under the assumptions that the individual net losses are bivariate upper-tail independent, identically distributed random variables and are independent, identically distributed random variables respectively about discrete time risk model. It futher shows that bivariate upper-tail independent, identically distributed discrete time risk model is more general, and is more advantageous to solve the problem in the insurance.