Optimal risk control and dividend distribution for a financial corporation with policy constraints

We study a model of a corporation which has possibility to choose various production/business policies with different expected profits and risks. In the model there are restrictions on the dividend distribution rates, as well as restrictions on the risk the company can undertake. The objective is to maximize the expected present value of the total dividend distributions. We outline the corresponding Hamilton-Jacobi-Bellman equation and compute explicitly the optimal return function and determine the optimal policy. As a consequence of these results the way the dividend rate and business constraints affects the optimal policy is revealed. In particular we show that under certain relationship between the constraints and the exogenous parameters of the random processes governing the returns, some business activities might be redundant, i.e., under the optimal policy they will be never used in any scenario.