论文标题
修改了随机控制问题的MSA
A modified MSA for stochastic control problems
论文作者
论文摘要
连续近似的经典方法（MSA）是解决随机控制问题的迭代方法，并源自Pontryagin的最佳原理。众所周知，MSA可能无法收敛。使用对向后随机微分方程（BSDE）的仔细估计，本文提出了对MSA算法的修改。该修改后的MSA显示出在漂移和扩散系数中控制的一般随机控制问题。在一些其他假设下，显示了收敛速率。结果是有效的，而无需限制控制问题的时间范围，与基于前向后随机微分方程理论的迭代方法相反。
The classical Method of Successive Approximations (MSA) is an iterative method for solving stochastic control problems and is derived from Pontryagin's optimality principle. It is known that the MSA may fail to converge. Using careful estimates for the backward stochastic differential equation (BSDE) this paper suggests a modification to the MSA algorithm. This modified MSA is shown to converge for general stochastic control problems with control in both the drift and diffusion coefficients. Under some additional assumptions the rate of convergence is shown. The results are valid without restrictions on the time horizon of the control problem, in contrast to iterative methods based on the theory of forward-backward stochastic differential equations.
