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 generalize the classical ones, the necessary condition for the optimality of an admissible control is also sufficient.

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