Optimal Dividend Strategy In Compound Binomial Dual Model With Bounded Dividend Rates And Periodic Dividend Payments

This paper discusses the problem of optimal dividend payment in compound binomial dual model with bounded dividend rates and periodic dividend payments.Through transforming the value function, we obtain some properties of the optimal dividend payment strategy, and show that the optimal value function is the unique solution of a discrete Hamilton-Jacobi-Bellman equation. Meanwhile, a simple algo-rithm is obtained for the optimal strategy and the optimal value function. According to the properties of the optimal dividend strategy,an upper bound and a lower bound of the optimal value function are derived. Numerical examples are presented to illustrate the transformation method.The structure of the paper is as follows: In chapter 2, we introduce the model and present a rigorous mathematical formulation of the optimization problem. In chapter 3, we discuss the character of the optimal strategy, and write down the HJB equation for the optimal value function. In chapter 4, according to the properties of the optimal dividend strategy, we offer an upper bound and a lower bound of the optimal value function. And numerical examples are presented to illustrate the algorithm.