The Optimal Dividend With Restricted Payment Scheme In The Continous-time Compound Binomial Model

In this paper, we study the optimal dividend problem with restricted payment scheme in the continuous-time compound binomial model. For the first time, the continuous-time compound binomial model is proposed by the G X Liu et al. This paper has modified the continuous-time compound binomial model and introduction of the dividend. The jump mechanism in this paper is different form that of Liu et al.To deal with the optimal dividend problem, we assume the follow rules: when the time arrives at non-integer points, dividends should be paid out at certain rate; when the time arrives at integer points, no dividend can be paid out if the models jump,amount of dividend can be paid out if the jump do not occur. Comparing with other papers, both continuous and discrete parts are in the value function.The paper is organized as follows. The Section 1 is preface. In Section 2, we formulate the problem. In Section 3, we discusses some properties of the value function. In Section 4, we derive the HJB equation and prove that the solution which satisfy HJB equation is the value function. Moreover, we obtain the optimal dividend strategy. In Section 5, we solve this equation, some time-delay integral equation are obtained. In Section 6, we summarize some results.