Optimal Dividend Strategy In Discrete Sparre Andersen Model

We consider the discrete Sparre Andersen risk model and its derivative models by anew setting up the initial times, 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 functions is the unique bounded solution of a set of discrete HamiltonJacobi-Bellman equations. Moreover, we introduce Bellman’s recursive algorithm and o?er a simpler algorithm to obtain the optimal strategy and the optimal value functions. Our method is mainly to transform the value functions to the image function, and solve the value function by means of solving the image function.Numerical examples are presented to illustrate the advantage of transformation method.