On The Compound Markov Binomial Risk Model With Dividend Strategy

The dividend strategy of discrete time risk model is a research hotspot in actuarial literature. As a generalization of compound binomial model, compound Markov binomial model has been widely concerned because of dependency structure. Based on compound Markov binomial model with dividend strategy, this paper mainly focuses on Gerber-Shiu penalty function, and recursive formulae and defective renewal equations satisfied by the penalty function are derived. Our results generalize some known conclusions in the existing literature.This paper can be divided into four chapters:Chapter 1. As the introduction of this paper, it describes the classic compound binomial model and compound binomial model with dividend strategy, the compound Markov binomial model is also summarized.Chapter 2. In this chapter we investigate the compound Markov binomial model with stochastic premium income and constant dividend, the recursive formulae for the GerberShiu penalty function are obtained.Chapter 3. In this chapter we consider the compound Markov binomial model when the stochastic dividend barrier is zero, the defective renewal equations for the Gerber-Shiu penalty function are derived, which generalize some related study in existing literature.Chapter 4. This chapter studies the compound Markov binomial model with general stochastic dividend barrier. When the initial surplus less than the dividend barrier, we obtain linear equations for the Gerber- Shiu penalty function.