In Several Types Of Dependency Risk Model

The risk theory is the basic discipline of learning financial mathematics and the actuarial mathematics of insurance and its core is the study of the ruin theory. In this text, based on the classical risk model, we construct and research three kinds of new risk models with dependence. Finally we obtain some expressions or characters of the variables about ruin.Six chapters constitute this text.In the first chapter, we simply introduce the history, the present development of the risk theory and the main result, and we especially pay more attention on the classical risk model. Finally we present the main content of this text and the main result of my research.In the second chapter , we outline the knowledge about conditional expectation, Laplace transform, point process, martingale etc. We also outline some useful theorems. This knowledge is also the foundation of the text.In the third chapter, we study and construct a new double-multiple risk model with correlated claim arriving process. In the model, we consider that there are two kind of risk happened. One (main claim) results in the other (by-claim) and their arriving time is correlated. In the paper, we get ruin probabilities when beginning reserve is equal to zero and u given that main claims arrives by Poisson process and premium receiving by constant ratio. Finally we derive the ruin probabilities and Lundberg upper bound when premium receives by random way, and by the way we present both common proof and martingale proof.In the fourth chapter, we study a ruin model with dependence between claim sizes and claim intervals. In the model, we improve independence in classical risk model about claim sizes and claim intervals by dependence, and introduce a random variable A which compares with claim sizes. Finally we derive the ruin probabilities algorithms when premium arriving process is constant ratio and beginning reserve is zero, and generally when premium arriving process is Poisson process we get Laplace transform algorithms of ruin probabilities. In the fifth chapter, we study a ruin model with dependence between claim sizes and premium size and claim intervals. In this chapter, we improve the risk model from the other point of view based on chapter four. We construct the model by considering premium receiving randomly and claim intervals are affected by changes of claim size and premium size. We gain integral equations about this model.In the sixth chapter, we consider a discrete time renewal risk model under constant interest rate. We obtain recursive algorithm finite-time non-ruin probability, and finite-time non-ruin probability and its upper bound.