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Stochastic controls of fractional Brownian motion

  • Ikram Hamed EMAIL logo and Adel Chala
Published/Copyright: February 1, 2024

Abstract

We consider a stochastic control problem for a non-linear forward-backward stochastic differential equation driven by fractional Brownian motion, with Hurst parameter H ( 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.


Communicated by Vyacheslav L. Girko


Funding statement: This work is partially supported by The University of Biskra, Faculty of Exact Sciences and Sciences of Nature and Life, PRFU project No. COOL03UN070120220004.

Acknowledgements

The authors wish to thank the referees and editors for their valuable comments and suggestions which led to improvements in the document.

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Received: 2022-10-01
Accepted: 2023-07-04
Published Online: 2024-02-01
Published in Print: 2024-03-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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