Before revision: The least squares Monte Carlo algorithm has become a popular tool for solving stochastic control problems, mainly due to its ability to handle multiple stochastic state variables. However, a configuration that remains challenging is when dealing with high dimensional controls, due to the exponential complexity of grid search methods or the mathematical difficulty of deriving and solving high-dimensional first-order optimality conditions. This paper proposes an efficient least squares Monte Carlo algorithm that is suitable for handling high-dimensional controls. In particular, we first approximate backward recursive dynamic programs on a coarse grid of controls , then use a combined technique of local control regression and adaptive refinement grids to improve the optimal control estimates.
After revision: The least squares Monte Carlo algorithm has become popular for solving portfolio optimization problems. A simple approach is to approximate the value functions on a discrete grid of portfolio weights , then use a combined technique of local control regression and adaptive refinement grids to improve the optimal control estimates.