  We study a model of a corporation which has the 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, 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 affect the
optimal policy is revealed. In particular, we show that under certain
relationships between the constraints and the exogenous parameters of the
random processes that govern the returns, some business activities might be
redundant, that is, under the optimal policy they will never be used in any
scenario.
