Discrete Risk Model Risk Dependent Claims Bankruptcy Probability

This dissertation consists of four chapters, which is completed during my Master Degree of Science.Chapter One is a preface. It gives an introduction to the development and significance of risk theory as well as the ruin probability. It also introduces the background and the main ideas of this dissertation. In addition, some knowledge about heavy tails is presented at the end.Chapter Two mainly introduces the concept and basic property of a kind of function— Copulas which is used to describe the dependence structure of randomvariables. In addition, the Sklar's theorem and several useful Copulas are alsointroduced.Chapter Three investigates the ruin probability of a discrete time risk model under constant interest rate with heavy tails. Based on the model in Tang, Q.(2004), We propose an improved risk model in which the risks of the insurance company obey some kind of dependence structure in terms of Copulas. Under the assumptionthat the net loss of the insurance company within one year is sub-exponentially distributed, some simple asymptotic relations for the finite and infinite ruin probability of our model are derived and compared to existing results.In Chapter Four, we further discuss the ruin probability of a discrete time risk model under random interest rate with heavy tails. We also propose a generalized model in which the dependence structure of risks is determined by a certain Copulas function. Under the assumption that the net loss within one year issub-exponentially distributed and that the random interest satisfy some condition, we also give some precise asymptotic relations of the finite time ruin probability of the above model.