Mean-field optimal control problem of SDDES driven by fractional Brownian motion

• Autorzy: Douissi Soukaina , Agram Nacira , Hilbert Astrid

Identyfikatory

DOI

10.37190/0208-4147.40.1.9

• Języki publikacji: EN

Abstrakty

EN

We consider a mean-field optimal control problem for stochastic differential equations with delay driven by fractional Brownian motion with Hurst parameter greater than 1/2. Stochastic optimal control problems driven by fractional Brownian motion cannot be studied using classical methods, because the fractional Brownian motion is neither a Markov process nor a semi-martingale. However, using the fractional white noise calculus combined with some special tools related to differentiation for functions of measures, we establish necessary and sufficient stochastic maximum principles. To illustrate our study, we consider two applications: we solve a problem of optimal consumption from a cash flow with delay and a linear-quadratic (LQ) problem with delay.

Słowa kluczowe

EN

mean-field; stochastic delayed differential equations; fractional Brownian motion; stochastic maximum principles

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2020
• Tom: Vol. 40, Fasc. 1
• Strony: 139--158
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Douissi Soukaina

• Laboratory LIBMA, Faculty Semlalia, University Cadi Ayyad, Boulevard Prince My Abdellah, 40000 Marrakech, Morocco

autor

Agram Nacira

• Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, N-0316 Oslo, Norway

autor

Hilbert Astrid

• Department of Mathematics, Linnaeus University, SE-351 95 Växjö, Sweden

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).