论文标题
关于向后双随机系统的平均场控制问题
On mean-field control problems for backward doubly stochastic systems
论文作者
论文摘要
本文涉及平均场类型的向后双随机微分方程的随机控制问题，其中系数函数取决于状态过程和控制过程的关节分布。我们获得了随机最大原理，该原理是最佳控制的必要条件，并且在适当条件下也证明了它的功能。作为一种副产品，我们证明了一种均值的均值完全耦合前回向的双重随机微分方程自然而然地由控制问题引起的，这本身就是感兴趣的。提供了一些示例，以说明我们结果在控制标量相互作用类型和一阶相互作用的类型中的应用。
This article is concerned with stochastic control problems for backward doubly stochastic differential equations of mean-field type, where the coefficient functions depend on the joint distribution of the state process and the control process. We obtain the stochastic maximum principle which serves as a necessary condition for an optimal control, and we also prove its sufficiency under proper conditions. As a byproduct, we prove the well-posedness for a type of mean-field fully coupled forward-backward doubly stochastic differential equation arising naturally from the control problem, which is of interest in its own right. Some examples are provided to illustrate the applications of our results to control problems in the types of scalar interaction and first order interaction.
