Random Discrete Interest Rate Risk Model

Many insurance companies use risk theory to mode] the surplus process. Usually ,ruin happens when the surplus becomes negative . Some effects such as the force of interest have to be considered. Some scholars have investigated the rule of risk and constructed a rigorous system in order to describe the regularity. The ruin probability attract a large number of attentions, especially the professional actuaries care much more for it.In this paper, we consider a class of discrete time risk model. Since time series is a discrete stochastic process and often model the complex correlativity, we resort to it as a useful tool. Martingale approach also plays key role in this article.In chapter 1,we present the dassical Cram r-Lundberg risk model . Some definitions and theorems are given in this chapter.In chapter 2,we find the upper bounds for ruin probabilities when the gains of insurance firm become dependent. We assume that the gain,the difference between premium and claim, behave according to a time series model. Through the martingale technique ,we get some results concerning the ruin probabilities.Several examples are giving to understanding the Basic Theorem .In the end of this chapter,we obtain some extensions of classic model.Chapter 3 is prepared for the next part. We investigate some properties of risk model under a stochastic interest force.Chapter 4 appears as the core of this paper. Ruin probability is affected by dependent rates,whose variation is dominated by a recursive equation.A super-martingale makes the problem resolvable. Another method is a recursive technique associated with some integral equation.In addition,some simulations in this paper are presented for verifying the precision of corresponding upper bounds.