On The Expected Penalty Function For The Compound Markov Binomial Model With Random Income

Risk theory is the foundation in modern actuarial science, which helps the operation of insurance companies by establishing and analyzing stochastic risk models. As the generalization of classical compound binomial model, the compound Markov binomial model plays a crucial role in risk theory. In this paper, we mainly study the Compound Markov binomial model with random premium income, the defective renewal equations and the asymptotic equations for the unconditional and conditional Gerber-Shiu expected discounted penalty function are obtained, Furthermore, asymptotic expressions for some important ruin quantities such as ruin probability and deficit at ruin are also given.The paper is divided into three chapters.Chapter 1. The research background of the paper is briefly introduced, and more detailed exposition of the classical Compound Markov binomial model and some related results with random premiums are given.Chapter 2. The first section of this chapter introduces the basic structure of the model. In the second and third sections, the defective renewal equations of expected penalty function with initial state zero and 1 are obtained respectively. In the fourth section the defective renewal equations of the unconditional Gerber-Shiu expected penalty function are obtained.Chapter 3. Based on the results in the second chapter, this chapter studies the asymptotic expression for the expectation penalty function. By taking the special value of Gerber-Shiu expected penalty function, asymptotic expressions for some important ruin quantities such as ruin probability and surplus before ruin are also given.