Abstract
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.
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Dorroh, J.R., Ferreyra, G. & Sundar, P. A Technique for Stochastic Control Problems with Unbounded Control Set. Journal of Theoretical Probability 12, 255–270 (1999). https://doi.org/10.1023/A:1021761030407
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DOI: https://doi.org/10.1023/A:1021761030407