Types Of Dependent 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. Modern risk theory has been developed mainly via stochastic process of mathematical tools, which provides a manager who is serving in finance risk department with theory basis and practical guidance. In this text, the theory of classical martingale and stochastic point process are applied in studying three kinds of new risk models with dependence. Finally we obtain some expressions or characters of the variables about ruin.Five chapters constitute this textIn the first chapter, we simply introduce the history, the present conditions and the main results of the risk theory, 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 compound Poisson-Geometric distribution and process, expectation, point process, martingale and so on. This knowledge is also the foundation of the textIn the third chapter, we introduce a risk model, where the distribution of the time between two claim occurrences depends on the previous claim size. Furthermore we discuss the two type-insurance risk model and derive analytical expressions for the Laplace transform of the non-ruin function.In the fourth chapter, we consider the common shock risk model and analyze and discuss the new model. Finally we attain the upper bounds of the ruin probability and we investigate the impact of dependence structure on the ruin probability through make a comparison about Lundberg exponent between dependence and independence structure.In the fifth chapter, we consider the compound Poisson-Geometric process risk model with dependence. we attain some basic properties and upper bounds of the ruin probability. Finally we also investigate the impact of dependence structure on the ruin probability.