Two Classes Of Discrete Time Risk Models With Random Premium Income

In the early risk theory,it is assumed the premium in unit time is 1 or a general positive integer in the discrete time risk model.However,the premium income is random in the pratical insurance.Therefore,more and more actuarial researchers focus on the models with random premium.In this paper we will study the two classes of compound binomial risk model with random premium income.The objects is to study the joint distribution of the surplus and deficit before ruin and the generalized expected discounted penalty function,and some theoretical results are obtained.This thesis is divided into three chapters.Chapter 1.This chapter first briefly introduces the significance of risk theory.After that,the discrete time risk models with cross claim,general premium income and random premium income are introduced concretely,and some basic results of these models are given.Chapter 2.This chapter studies the compound binomial risk model with random premium income and cross claim.The model involves four classes of claim,including two main claims and two by-claims.Every main claim must produce a by-claim and the occurrence of the by-claim may be delayed.Section 1 gives the discrete time renewal risk model involving cross claims.In section 2,we obtain the joint distributions of the surplus before ruin and deficit at ruin.In section 3,by inversing probability generating functions,we derive the analytic expression of the ultimate ruin probability.Chapter 3.This chapter studies the discrete time risk model which involves random premium income.Section 1 gives the compound binomial model and makes a simple description of it,then introduces the generalized expected discounted penalty function.In section 2,by discussing the root of the Lundberg’s fundamental equation,we obtain an explicit expression for the generalized expected discounted penalty function.We then examine the original expected discounted penalty function and derive its generating functions.