SIAM Journal on Control and Optimization, Volume 61, Issue 6, Page 3467-3500, December 2023.
Abstract. We consider the optimal control problem of stochastic evolution equations in a Hilbert space under a recursive utility, which is described as the solution of a backward stochastic differential equation (BSDE). A very general maximum principle is given for the optimal control, allowing the control domain to not be convex and the generator of the BSDE to vary with the second unknown variable [math]. The associated second-order adjoint process is characterized as a unique solution of a conditionally expected operator-valued backward stochastic integral equation.

中文翻译：

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利用递归函数优化控制随机演化方程的极大值原理

SIAM 控制与优化杂志，第 61 卷，第 6 期，第 3467-3500 页，2023 年 12 月。
摘要。我们考虑递归效用下希尔伯特空间中随机演化方程的最优控制问题，将其描述为向后随机微分方程（BSDE）的解。对于最优控制，给出了一个非常通用的最大原理，允许控制域不是凸的，并且 BSDE 的生成器随第二个未知变量 [math] 变化。相关的二阶伴随过程的特征是条件期望算子值逆向随机积分方程的唯一解。