OPTIMAL DIVIDEND AND REINSURANCE UNDER THRESHOLD STRATEGY

We consider the optimal dividend and reinsurance problems in this article, where the dividend strategy is the threshold strategy and the reinsurance is the proportional reinsurance. Despite the fact that the barrier strategy has its popularity in theoretical research, such a strategy has little practical acceptance as it will lead to the certainty of ultimate ruin. A modified version of the barrier strategy is the threshold strategy which assumes that dividends are paid at a rate smaller than the rate of premium income whenever the surplus is above some threshold level, and that no dividends are paid out whenever the surplus is below the threshold level. In this article, we consider two cases of the threshold strategy. One is the threshold strategy without barrier, and the other is the threshold strategy with barrier. The first case generalizes and corrects part of results in [16]. In the second case, we use the stochastic control theoretic techniques, to find the value function as well as the optimal investment-reinsurance policy in closed form.