ABSTRACT We study linear‐quadratic optimal control problems of mean‐field controlled stochastic differential systems driven by fractional Brownian motions with Hurst parameter with deterministic coefficients. By a variational method, we derive the optimality system, which is a mean‐field forward‐backward stochastic differential equation. When the diffusion term satisfies certain conditions, using a decoupling technique and Malliavin calculus, we obtain two Riccati differential equations that are uniquely solvable under certain conditions. Then we derive a feedback representation for the optimal control and the explicit solution of the mean‐field backward stochastic differential equation without Malliavin derivatives.
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Optimal Control Applications and Methods
Changchun University of Technology
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