A Recursive Dual Method for Stochastic Control and Its Applications in Finance

We use the information relaxation technique to develop a value-and-policy iterative method to solve SDP problems. Each iteration generates a confidence interval estimate for the true value function so we can use the gap... [ view full abstract ]

We use the information relaxation technique to develop a value-and-policy iterative method to solve SDP problems. Each iteration generates a confidence interval estimate for the true value function so we can use the gap between the upper and lower bounds to access the quality of the policy. We show that the resulted sequences of suboptimal policies converge to the optimal one within finite number of iterations. A regression-based Monte Carlo algorithm is introduced to overcome the dimensionality curse in the implementation of this approach for high dimensional cases. As numerical illustrations, we apply the algorithm to optimal order execution problem.