随机最优控制问题广泛出现在金融、物理、工程及科学中，随着越来越多的学者们对带随机系数或者不确定输入的偏微分方程数值解的关注，随机最优控制问题的数值近似也渐渐引起了学术界的关注。在研究随机微分方程数值解时，Monte Carlo方法起到了很大的作用，近几年出现的多水平Monte Carlo/quasi-Monte Carlo方法在这方面展示了更大的优越性。而随机最优控制问题的数值近似，离不开随机微分方程的数值模拟。. 本项目拟结合多水平Monte Carlo/quasi-Monte Carlo法和有限元法来研究随机最优控制问题、椭圆随机最优控制问题和抛物随机最优控制问题的数值近似，分别考虑控制变量确定、不确定以及分布参数控制和边界控制等问题，期望得到相应问题的高效数值方法，数值方法的复杂性和数值解的收敛性等方面的结论。

Stochastic optimal control problems are widely used in finance, physics, engineering and science. With more and more scholars paying attention to the numerical solutions of PDEs with stochastic coefficients or uncertain inputs, the numerical approximation of stochastic optimal control problems have gradually attracted the attention of scholars. In the numerical approximation of stochastic PDEs, Monte Carlo methods play an important role. In recent years, the multi-level Monte Carlo/quasi-Monte Carlo methods have shown greater superiority in this respect. The numerical approximation of stochastic optimal control problems can not be separated from the numerical simulation of stochastic differential equations.. This project intends to study the numerical approximation of stochastic optimal control problems, elliptic and parabolic stochastic optimal control problems by combining multilevel Monte Carlo/quasi-Monte Carlo methods and finite element methods. The problems of deterministic and random control variables, distributed control and boundary control will be considered respectively. Some high efficient numerical methods for corresponding problems, conclusions of complexity and convergence results for different numerical methods will be obtained.