Study On Discrete-time Ruin Problem With Interest

This thesis studies discrete-time risk model, in which the net loss processes are as-sumed to have an AR(1) structure and the interest rates follow a Markov chain. Our goal is to discuss the ruin probabilities in this model. Firstly, we present the clas-sic Lundberg-cramer risk models and the methods to research the modern ruin theory. Some general discrete-time risk models are also given. To be more important, in the thesis, we obtain the recursive and integral equations for the ruin probabilities and the upper bounds for ruin probabilities by the inductive approach and the martingale ap-proach.