The Optimal Dividend In The Compound Binomial Dual Model

This paper discuss the problem of the optimal dividend-payments in compound binomial dual model. We describe a fully discrete dual model and obtain the optimal value function by analysing the HJB equation. We using Bellman recursive algorithm to calculate the optimal value function and the optimal dividend strategy. Then we prove two functions approach of the optimal value function. In addition, we use numerical examples to illustrate authenticity of the algorithm.In order to be more realistic, then we consider the optimal dividend problem with capital injections with proportional transaction costs based on the discrete model, where the dividend discount rate is random variables. We describe the dividends and capital injections are respectively two {Ft} adapted random sequences.By transforming the value function into the corresponding image function, we analyze and discuss the properties of image function and the calculation method for optimal dividend strategy. According to the numerical solutions, we also ?nd that when transaction costs less than a certain proportion for the injections the value of the optimal strategy is greater than the case without injection.