Existence results for optimal stochastic controls

The paper treats the problem of existence of optimal controls for a large class of delay-differential Itô equations, where the control is a nonanticipative measurable function of the trajectory (the case of complete information). The technique, which seems simpler than past approaches to the problem, requires the use of results on weak convergence of measures, and gives fairly general results. Control can be either over a fixed-time interval, or it can terminate when a target set is reached, and there can be additional (almost everywhere continuous) side constraints.