On Some Classes Of Discrete Time Risk Models With Dependence And Random Premium Incomes

Modern risk theory plays a crucial role in actuarial theory, and the research on risk theory affects the development of insurance. The discrete time renewal risk process has been attractive field in modern risk theory. In this paper, we mainly generalize the classical compound binomial risk model by proposing three classes of the discrete time risk models with dependence and random premium incomes. We mainly study the analytic expressions for the probability generating functions of Gerber-Shiu penalty functions and the defective renewal equations satisfied by penalty functions respectively.This thesis is divided into four chapters.Chapter 1. As the introduction of this article, this chapter first makes a brief summary of the classical compound binomial risk model, the classical compound Poisson risk model and their related generalized forms, then introduces the three important models which will be discussed in this paper.Chapter 2. This chapter studies the compound binomial risk model with delayed claims and random premium incomes. The basic model is given in section 1. In section 2, by introducing an auxiliary risk process, we obtain the probability generating function of penalty function. In section 3, we derive the defective renewal equation satisfied by the penalty function.Chapter 3. In this chapter, we consider the random threshold and change the assumptions at the initial time based on the model in chapter 2, then the model is further extended. We obtain the analytic expressions for the probability generating function of penalty function of this model. Then the defective renewal equation satisfied by the penalty function is derived by using the discrete operator.Chapter 4. This chapter studies a discrete time dependent renewal risk model with Poisson premium incomes. The dependent relationship between claim time intervals and claim sizes is consisted of m probability density functions. In this context, we get the probability generating function of penalty function in section 2, section 3 proves the defective renewal equation.