The main goal of the proposed research is to further develop the linear programming approach to optimal stochastic control and to make this solution technique applicable to all types of stochastic control problems, including stopping time problems, impulse control, singular control and adaptive control problems. This approach will also be used to analyze complex models in areas as diverse as mathematical finance and quality control.
A major benefit of the LP approach is that it naturally lends itself to numerical methods. Two approaches will be pursued: a discretization technique and the method of moments. A significant part of the grant will be devoted to implementing and testing numerical schemes using linear programming software to compute optimal controls.