Ruin Problems With Dependent Rates Of Interest

In risk theory, ruin probability is a main research area. Ruin probability and related problems have received increasingly large amounts of attention. And the effects of interest on ruin problems have been discussed in several references.The effects of a constant rate and iid rates on rain problems have been studied. However, the above assumptions are not particularly realistic since rates of interest are usually statistically dependent over time.In this paper, we study ruin problems in two generalized risk modles with dependent rates of interest. The convergence of the discounted surplus is proved by using the martingale method. The integral equations satisfied by the ruin probability, the distribution of surplus just before ruin, the distribution of surplus immediately after ruin and the joint distribution of surplus immediately before and after rain are derived, respectively.