Research On The Discrete Model And Recursive Calculation In Risk Theory

This thesis is finished during my graduate student program to Master Degree of Science. Risk theory is the system of mathematical statistics analysis on all kinds of risk, which is the main part of insurance. This thesis is mainly about discrete ruin probability model and recursive calculation of claims. It consists of three chapters.Chapter 1 is mainly about the discrete risk model and its limit theory.In this chapter, firstly, we construct a new discrete ruin model with diffusion. Secondly, we study the ruin probability and the Lundberg upper bound of this model. Finally, we discuss the limit theory of risk model.Chapter 2 is mainly about recursive calculation of claims. In this chapter, firstly, we review the Panjer's recursive calculation, when condition 2.1 is satisfied,and the generalization of Panjer's recursive calculation, which satisfies condition2.2 or 2.3.Secondly, we obtain condition 2.4, which generalizes the condition 2.2 and 2.3, and study the recursive calculation under condition 2.4. Finally, the application of recursive calculation on compound distribution is given, which satisfies condition 2.3.Chapter 3 is mainly about some further study of recursive calculation in risk theory. In this chapter, firstly, we study the recursive calculation of compound distribution when condition 3.1 is satisfied. Secondly, we discuss the Markov recursion and the relation between Markov's recursion and Panjer's recursion. Thirdly, we study the recursive calculation of stop-loss reinsurance. Finally, the application of recursion is given, which satisfies condition 3.1.