Stochastic controls of fractional Brownian motion. (English) Zbl 1533.93842
Summary: We consider a stochastic control problem for a non-linear forward-backward stochastic differential equation driven by fractional Brownian motion, with Hurst parameter \(H\in (0,1)\), in the case where the set of the control domain is convex. We provide an estimation of the solution and establish the necessary and sufficient optimality conditions in the form of the stochastic maximum principle. We apply the theory to solve a linear quadratic stochastic control problem.
MSC:
| 93E20 | Optimal stochastic control |
| 49N10 | Linear-quadratic optimal control problems |
| 93C10 | Nonlinear systems in control theory |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60G22 | Fractional processes, including fractional Brownian motion |
Keywords:
fractional Brownian motion; stochastic maximum principle; generalized Itô formula; optimal controlReferences:
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