Tompaidis, Efstathios, 1967-2010-12-022010-12-022017-05-112010-12-022010-12-022017-05-112010-08August 201http://hdl.handle.net/2152/ETD-UT-2010-08-1557textI develop a numerical method that combines functional approximations and dynamic programming to solve high-dimensional discrete-time stochastic control problems under general constraints. The method relies on three building blocks: first, a quasi-random grid and the radial basis function method are used to discretize and interpolate the high-dimensional state space; second, to incorporate constraints, the method of Lagrange multipliers is applied to obtain the first order optimality conditions; third, the conditional expectation of the value function is approximated by a second order polynomial basis, estimated using ordinary least squares regressions. To reduce the approximation error, I introduce the test region iterative contraction (TRIC) method to shrink the approximation region around the optimal solution. I apply the method to two Finance applications: a) dynamic portfolio choice with constraints, a continuous control problem; b) dynamic portfolio choice with capital gain taxation, a high-dimensional singular control problem.application/pdfengHigh-dimensional stochastic control problemsDynamic portfolio choiceApproximationsthesis2010-12-02