We consider the compound binomial model,and assume that dividends are paid to the shareholders according to an admissible strategy with dividend rates bounded by a constant.The company controls the amount of dividends in order to maximize the cumulative expected discounted dividends prior to ruin.We show that the optimal value function is the unique solution of a discrete HJB equation.Moreover,we obtain some properties of the optimal payment strategy,and offer a simple algorithm for obtaining the optimal strategy.The key of our method is to transform the value function.Numerical examples are presented to illustrate the transformation method.
