Regression methods forstochastic controlproblems and theirconvergence analysis
In this paper we develop several regression algorithms for solvinggeneral stochastic optimal control problems via Monte Carlo. Thistype of algorithms is particularly useful for problems with a highdimensionalstate space and complex dependence structure of the underlyingMarkov process with respect to some control. The main ideabehind the algorithms is to simulate a set of trajectories under somereference measure and to use the Bellman principle combined with fastmethods for approximating conditional expectations and functional optimization.Theoretical properties of the presented algorithms are investigatedand the convergence to the optimal solution is proved undersome assumptions. Finally, the presented methods are applied in anumerical example of a high-dimensional controlled Bermudan basketoption in a financial market with a large investor.