A Stochastic Maximum Principle for General Mean-Field Systems
A Stochastic Maximum Principle for General Mean-Field Systems
复制标题
DOI：
10.1007/s00245-016-9394-9
复制
发表时间：
2016-11
影响因子：
1.8
通讯作者：
R. Buckdahn;Juan Li;Jin Ma
中科院分区：
文献类型：
--
作者：
R. Buckdahn;Juan Li;Jin Ma
本文研究了一类一般平均场随机微分方程的最优控制问题，其中系数既非线性地依赖于状态过程，又非线性地依赖于状态过程的规律。特别地，我们假设控制集是一个不一定是凸的一般开集，并且系数仅在控制变量上连续，没有任何进一步的正则性或凸性。我们通过考虑这种设置中的二阶变分方程和相应的二阶伴随过程来验证Peng（SIAM J Control Optim 2（4）：966-979，1990）的方法，并且我们将Buckdahn等人的随机最大值原理（Appl Math Optim 64（2）：197-216，2011）扩展到这种一般情况。
In this paper we study the optimal control problem for a class of general mean-field stochastic differential equations, in which the coefficients depend, nonlinearly, on both the state process as well as of its law. In particular, we assume that the control set is a general open set that is not necessary convex, and the coefficients are only continuous on the control variable without any further regularity or convexity. We validate the approach of Peng (SIAM J Control Optim 2(4):966–979, 1990) by considering the second order variational equations and the corresponding second order adjoint process in this setting, and we extend the Stochastic Maximum Principle of Buckdahn et al. (Appl Math Optim 64(2):197–216, 2011) to this general case.