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Mean-field optimal control problem of SDDES driven by fractional brownian motion
University Cadi Ayyad, Morocco.
University of Oslo, Norway.
Linnaeus University, Faculty of Technology, Department of Mathematics. (DISA-DSM)ORCID iD: 0000-0002-5362-6475
2020 (English)In: Probability and Mathematical Statistics, ISSN 0208-4147, Vol. 40, no 1, p. 139-158Article in journal (Refereed) Published
Abstract [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 one half. Stochastic optimal control problems driven by fractional Brownian motion can not 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 the differentiation for functions of measures, we establish and prove 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.

Place, publisher, year, edition, pages
Politechnika Wroclawska, Oficyna Wydawnicza , 2020. Vol. 40, no 1, p. 139-158
National Category
Other Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-93443DOI: 10.37190/0208-4147.40.1.9ISI: 000588619400009Scopus ID: 2-s2.0-85090254226OAI: oai:DiVA.org:lnu-93443DiVA, id: diva2:1423641
Available from: 2020-04-15 Created: 2020-04-15 Last updated: 2022-02-23Bibliographically approved

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Agram, NaciraHilbert, Astrid

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