Optimal Dividend And Investment Problem In The Continuous-Time Compound Binomial Model

In this paper,we study the problem of the optimal dividend and capital injection of the continuous-time compound binomial model.Not too long ago most writers mainly study the situation that is no condition to bear all the deficit.Now we mainly study the restriction of the capital injection strategy under the restricted dividend strat-egy.In considering the difference between the maximum cumulative discounted dividend and cumulative discounted cash injection,with the characteristic of the continuous-time compound binomial model,we get the value function,and we proof the basic properties of the value function and the HJB equation.