This paper applies the method of backward stochastic differential equations (BSDEs) to study the bang–bang optimal stochastic control problem, where the optimal control is of the feedback form and the final cost functional is given by a symmetric function. In addition to obtaining the existence of the optimal control, we also give the explicit representation of the optimal control and the optimal value function of the stochastic control problem by the explicit solution of nonlinear BSDEs with symmetric terminal condition.

中文翻译：

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一类具有对称成本函数的最优随机控制问题的 Bang-bang 控制

本文应用后向随机微分方程（BSDEs）的方法研究bang-bang最优随机控制问题，其中最优控制是反馈形式，最终成本函数由对称函数给出。除了得到最优控制的存在性外，我们还通过具有对称终端条件的非线性BSDEs的显式解给出了最优控制的显式表示和随机控制问题的最优值函数。