The Optimal Dividend Problem in Dual Model with Capital Injections by Stochastic Interest Rates

Under the dividend bounded, the problem of optimal dividend payment in compound binomial dual model with proportional transaction cost capital injections and stochastic interest rates was discussed. It was proved with the fixed-point principle of contraction mapping that the optimal value function of this optimal dividend problem was the unique solution to a discrete Hamilton-Jacobi-Bellman(HJB) equation. The algorithm was obtained for the optimal dividend strategy and the optimal value function. According to some properties of the dividend strategy, the upper and lower bounds of the optimal value function were derived, and the numerical solutions to the optimal value function and the optimal dividend strategy was obtained with the Bellman recursive algorithm, and the optimal dividend algorithm was obtained. The numerical result shows that the optimal dividend strategy is effective. A theoretical basis for the decision-maker to make dividend policy in consideration of the normal operation of the company and interests of shareholders is provided.