Forward-Backward Stochastic Differential Equations and Controlled McKean Vlasov Dynamics
Forward-Backward Stochastic Differential Equations and Controlled McKean Vlasov Dynamics
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DOI：
10.1214/14-aop946
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发表时间：
2013-03
影响因子：
2.3
通讯作者：
R. Carmona;F. Delarue
中科院分区：
文献类型：
--
作者：
R. Carmona;F. Delarue
本文的目的是对McKean-Vlasov型非线性随机动力系统的最优控制问题进行详细的概率分析。由于最近对平均场博弈的兴趣，我们强调了两组问题之间的联系和差异。我们证明了随机极大原理的一个新版本，并给出了最优控制存在的充分条件。并给出了最优解存在的充分条件。最后，我们证明了控制问题的解提供了具有平均场相互作用的大型随机控制系统在服从共同策略时的近似平衡点。
The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of McKean–Vlasov type. Motivated by the recent interest in mean-field games, we highlight the connection and the differences between the two sets of problems. We prove a new version of the stochastic maximum principle and give sufficient conditions for existence of an optimal control. We also provide examples for which our sufficient conditions for existence of an optimal solution are satisfied. Finally we show that our solution to the control problem provides approximate equilibria for large stochastic controlled systems with mean-field interactions when subject to a common policy.