Near optimization of stochastic dynamic systems by decomposition and aggregation

The paper is concerned with the reduction of a class of stochastic optimal control problems to simpler problems by using decomposition and aggregation. Decomposition is shown to provide a good approximation when the system dynamics involve nearly decomposable matrices or variables with strong and weak interactions. Aggregation provides a good approximation if each decomposed matrix has one or more dominant eigenvalues. It is shown how one can construct nearly optimal controls for the given system from the optimal solutions of the simpler reduced problems. The results extend the corresponding results obtained in a deterministic environment. The results hold a significant promise in dealing with large dynamic stochastic macroeconomic problems.