A technique for stochastic control problems with unbounded control set (Q1283448)

A technique in the time domain for solving stochastic control problems with an unbounded control set is described. The technique is applied to a class of maximization problems that do not have optimal controls. For such a given problem, an extended problem is formulated which has the same value function as the original problem and for which there exist optimal controls that are expressible in simple terms. In this way, a sequence of suboptimal controls for the original problem is obtained. For this sequence the payoff functions approach the value function.