Abstract
AbstractWe study a stochastic control problem of mean‐field controlled stochastic differential systems driven by a fractional Brownian motion with Hurst parameter . As a necessary condition of the optimal control we obtain a stochastic maximum principle. The associated adjoint mean‐field backward stochastic differential equation driven by a fractional Brownian motion and a classical Brownian motion. Applying the stochastic maximum principle to a mean‐field stochastic linear quadratic problem, we obtain the optimal control and prove that the necessary condition for the optimality of an admissible control is also sufficient under certain assumptions.
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