A Technique for Stochastic Control Problems with Unbounded Control Set
We describe a change of time technique for stochastic control problems with unbounded control set. We demonstrate the technique on a class of maximization problems that do not have optimal controls. Given such a problem, we 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 we mean a sequence of controls for which the payoff functions approach the value function.
Publication Source (Journal or Book title)
Journal of Theoretical Probability
Dorroh, J., Ferreyra, G., & Sundar, P. (1999). A Technique for Stochastic Control Problems with Unbounded Control Set. Journal of Theoretical Probability, 12 (1), 255-270. https://doi.org/10.1023/A:1021761030407