Mean-field SDE driven by a fractional Brownian motion and related   stochastic control problem
  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. 
Rainer Buckdahn and Shuai Jing
math.OC math.PR