Discrete Time Risk Model With A Variable Interest Rate Bankruptcy

In ((Actuarial Mathematics)) N. L .Bower etc. specially have discussed the discrete time risk model in which the premium income of per unit time is regarded as a constant, the claim amount of each period time is regarded as independent and identically distributed random variable. H. Yang (1999) gets the non-exponential bounds for ruin probability with constant interest by use of martingale methods. Under the discrete time risk model with constant interest, SUN Li-juan and GU Lan (2002) have discussed some ruin problems which are about the distributions of the surplus immediately before ruin and the time of the severity of ruin. Because of the effects of the timing of payments and interest on the surplus process, J. Cai(2002) considers the two factors , then discusses the problems of the ruin probability under the two generalized discrete time risk models respectively when the rates of interest are independent and identically distributed random variables and have a dependent autoregressive structure. In this paper when the rates of interest{rn,n = 1,2,...}are i.i.d.and have a dependent autoregressive structure rn = arn-1 +Wn, we get the formulas of the distributions of the surplus immediately before ruin and the time of the severity of ruin under two generalized discrete time risk models. Secondly in this paper we discuss the common survival probability in finite time period under the generalized compound Poisson risk model in which the premium income process is a Poisson process and in case of Gamma's claim amounts, then we get more satisfied expressions.