Study Of Several Types Of Bankruptcy With Interest Rate Risk Model

In this paper, we discussed some problems of three special risk models with interest by recursive method and Martingale method.In the second chapter, we discussed the continuous-time renewal risk model with interest , and its premium is a homogeneous-Poisson process. This model is. amelioration to the renewal risk model of Jun Cai, David C.M.Dickson. In Jun Cai, David C.M.Dickson model, The premium is a constant and continuous. But in real world, more and more companies receive their premium stochastic. So in this chapter, we assume the premium is a homogeneous-Poisson process basing the renewal risk model of Jun Cai, David C.M.Dickson. First, we discussed the upper-bound of ruin probability by recursive method and martingale method. Then we analysis the deficit at ruin by recursive method, and the surplus prior to ruin. In the end, we discussed the joint distribution of the deficit at ruin and the surplus prior to ruin.In the third chapter, we discussed discrete-time risk model with constant interest and its premiums are independent and the same distribution stochastic serial. In this model, we assume the premiums are variable with the same distribution. First, we discussed the integral equation of the survival probability by recursive method. Then we discussed the deficit at ruin and the surplus prior to ruin. In the forth chapter, we analysis discrete-time risk model with stochastic interest and its premium are independent serials with same distribution. Interests are often different in every period, so we betterment the model in the base of third chapter, we assume that interests are independent and the same distribution serial. We get the upper bound of ruin probability by martingale method and recursive method separately. Then we assume the distribution of interest and net loss in every period, computing the upper bound of ruin probability with real numbers. We can get a conclusion that upper bounds derived by recursive method are tighter than those derived by the martingale method.