The Research On Correlated Risk Models And Related Problems

In classical risk model and many extended risk models, the property of independence is an important assumption. In most actuarial literature to risk theory, the assumption of independence between classes of business in an insurance book is always made. In practice, however, there are certain corrlelation between classes of business because common factor which cause risl exists, thus comparing with the classical risk model, it is more realistic to consider dependent risl models. Recently, many scholars have made some recearches on the correlated risk models. In this text, we construct and research three kinds of risk models with the distribution of the time between two claim occurrences denpeding on the previous claim size. Finally, we obtain some expressions or characters of the variables about ruin.We arrange paper as following: In Chaper 1, we simply introduce the history, the present development of the risk theory and the main result, and we especially paymore attention on the classical risk mode. 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, point process, Laplace transform etc. We also ouline some useful theorems. This knowledge is also the foundation of the text. In the third chapter, we consider the dependent risk model given by Albrecher in 2004 and study the generalized Gerber-Shiu function of this model. Explicit expression for the Laplace transform is derived. And then the result is show by an example. In the fourth chapter, we consider the dependent risk model which is an extendability of the model given be Albrecher in 2004. we consider a generalization of the classical ruin model, where the income is a Poisson process and the distribution of the time between two claim occurrences depends on the previous claim size. This model is more appropriate than the classical ruin model. Explicit expression for the generating function of Gerber-Shiu expected discounted penalty function are derived. Then, a similar model is discussed. Finally, the results are showed by two examples. In the fifth chapter, we study an risk model with the income size is an compound Poisson process and the distribution of the time between two claim occurrences depends on the previous claim size.