Abstract: In this paper, a gradient projection optimization method is applied to solve a class of stochastic optimal control problems. The Monte Carlo method is a common method to deal with stochastic optimal control problems, but it has a notoriously slow convergence rate. We choose the Quasi-Monte Carlo method with faster convergence.  In order to make the random sampling dimensions and time discrete points independent, we use the Karhunen-Lo${\grave{\rm e}}$ve truncation for the Brown motion. Sobol sequences of  the Quasi-Monte Carlo method are used for sampling. The error of numerical approximation is presented, and the effectiveness of the method is verified by numerical experiments.

Key words: Stochastic differential equation, Optimal control , $Karhunen-Lo\grave{e}ve$ expansion, Quasi-Monte Carlo method