The Optimal Dividend Problem For The Continuous-Time Compound Binomial Model With A Penalty Function At Ruin

In this paper,we study the optimal dividend problem for the continuous-time compound binomial model with a penalty function at ruin.The continuous-time compound binomial model is firstly proposed by Liu G X,Wang Y,Zhang B.The model that we are considering is another continuous version of the discrete-time compound binomi-al model.As Dickson,Water said,the shareholders should have the obligation to pay the deficit in ruin.Therefore,under the restricted dividend policy,we maximize the expected difference of the cumula-tive discounted dividends until the time of ruin and the discounted deficit at the moment of ruin.Under the frame of continuous-time compound binomial model,we study the basic properties of the value function,and prove the dynamic programming principle,so we obtain the HJB equation,and the unique solution of the HJB equation is proved by the combination of the verification theorem.