标题： 具有二次生成器的均值场前向-后向随机控制系统的全局随机最大原理 显示英文标题

标题： A Global Stochastic Maximum Principle for Mean-Field Forward-Backward Stochastic Control Systems with Quadratic Generators

摘要： 我们的论文致力于研究彭的随机最大原理（SMP）对于由受控前向随机微分方程（SDE）作为动力学和受控后向SDE定义的代价泛函的随机控制问题。我们的研究结合了来自两方面的困难，一方面是因为SDE和后向SDE的系数是平均场类型（即它们不仅依赖于控制过程和解过程，还依赖于它们的分布），另一方面是因为BSDE的系数在$Z$上具有二次增长。我们的SMP是新颖的，它以一种远非微不足道的方式扩展了现有的SMP结果。 显示英文摘要

摘要： Our paper is devoted to the study of Peng's stochastic maximum principle (SMP) for a stochastic control problem composed of a controlled forward stochastic differential equation (SDE) as dynamics and a controlled backward SDE which defines the cost functional. Our studies combine the difficulties which come, on one hand, from the fact that the coefficients of both the SDE and the backward SDE are of mean-field type (i.e., they do not only depend on the control process and the solution processes but also on their law), and on the other hand, from the fact that the coefficient of the BSDE is of quadratic growth in $Z$. Our SMP is novel, it extends in a by far non trivial way existing results on SMP.