  We consider a stochastic optimal control problem in a market model with
temporary and permanent price impact, which is related to an expected utility
maximization problem under finite fuel constraint. We establish the initial
condition fulfilled by the corresponding value function and show its first
regularity property. Moreover, we can prove the existence and uniqueness of
optimal strategies under rather mild model assumptions. On the one hand, this
result is of independent interest. On the other hand, it will then allow us to
derive further regularity properties of the corresponding value function, in
particular its continuity and partial differentiability. As a consequence of
the continuity of the value function, we will prove the dynamic programming
principle without appealing to the classical measurable selection arguments.
