Stochastic problems with unbounded control set

Abstract

Describes a change of time technique for stochastic control problems with unbounded control set. The authors demonstrate the technique on a class of maximization problems that do not have optimal controls. Given such a problem, the authors introduce an extended problem which has the same value function as the original problem and for which there exist optimal controls that are expressible in simple terms. This device yields a natural sequence of suboptimal controls for the original problem. By this the authors mean a sequence of controls for which the payoff functions approach the value function.