分数布朗运动驱动的平均场SDE及其随机控制问题
Mean-field SDE driven by a fractional Brownian motion and related stochastic control problem
摘要：
研究了一类由分数布朗运动驱动的具有Hurst参数$H\in(1/2,1)$的平均场随机微分方程及其相关的随机控制问题.本文导出了经典布朗运动驱动下的Pontryagin型最大值原理和相应的伴随平均场倒向随机微分方程，并证明了在推广经典假设的条件下，容许控制的最优性的必要条件也是充分的.
英文摘要：
We study a class of mean-field stochastic differential equations driven by a fractional Brownian motion with Hurst parameter $H\in(1/2,1)$ and a related stochastic control problem. We derive a Pontryagin type maximum principle and the associated adjoint mean-field backward stochastic differential equation driven by a classical Brownian motion, and we prove that under certain assumptions, which generalise the classical ones, the necessary condition for the optimality of an admissible control is also sufficient.
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