With The Bankruptcy Probability Of Random Interference And Constant Interest Force Classical Risk Model

The main risk model that we consider in this paper is the renewal risk model, and all chapters in this paper are carried through based upon the heavy-tailed distribution (large claim). Considering that many researchers have not considered stochastic diffusion in the studies of risk theories, we think the risk models in some problems still have deficiency.In this paper, we will extend and improve the classical Cramer-Lundberg model in two aspects. First, stochastic diffusion{W(t),t>0} is introduced. W{t) is astandard Brown motion which stands for the uncertainty stochastic income and expenditure at the time t. At the same time, we introduce a constant interest force 8 > 0 which affects the risk process. Cramer-Lundberg model is changed into the form:In Chapter 2, we will discuss two-sided bounds for the ruin probability (u,c,T) of the risk model in finite time [0, T], where (u, c, T) is defined byWe get an estimate: , when n > NWhere 0<θ<1.In Chapter 3, we study the large deviation of the ordinary risk model. Underthe assumptions that the claim size is GERV (Generalized Extended Regularly Varying) class and safe load condition, we obtain the an estimate for the large deviation .The large deviation is about the centralization of random sum SN(t)γ > 0 and δ> 0 which are fixed,GERV class is a larger heavy-tailed distribution than ERV class, so the conclusion is an extension and improvement to Theory 1 in the literature [30].Ruin probability and large deviation play an important role in the risk theory. We expect that the research work of this paper is of not only academic value, but also strong applied potential.