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Sibirskii Zhurnal Industrial'noi Matematiki, 2022, Volume 25, Number 4, Pages 116–135
DOI: https://doi.org/10.33048/SIBJIM.2021.25.410 (Mi sjim1200) 		 
On optimal control in the problem of long-run tracking the exponential Ornstein—Uhlenbeck process

E. S. Palamarchukab

a Central Economics and Mathematics Institite RAS, Nakhimovsky prosp. 47, Moscow 117418, Russia
b Higher School of Economics, Pokrovsky bul. 11, Moscow 109028, Russia
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DOI: https://doi.org/10.33048/SIBJIM.2021.25.410
Abstract: We consider a problem of optimal tracking the exponential Ornstein—Uhlenbeck process. By change of variables, the linear-quadratic control system with discounting has been transformed into linear inhomogeneous system with random coefficients. For such a system, we obtain an optimal control law over an infinite time-horizon. The results are applied to derive an optimal control in the tracking problem with respect to criteria of long-term losses per unit of accumulated discount.
Keywords: linear stochastic controller, tracking, exponential Ornstein—Uhlenbeck process, discounting. .
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation AAAA-A21-121012090157-9
The work was carried out as part of the research work on the topic “Development of the Theory and Computer-Mathematical Tools for the Study of Socio-Economic Processes,” project no. AAAA-A21-121012090157-9.
Received: 11.04.2022
Revised: 16.06.2022
Accepted: 22.06.2022
English version:
Journal of Applied and Industrial Mathematics, 2022, Volume 16, Issue 4, Pages 720–736
DOI: https://doi.org/10.1134/S1990478922040135
Document Type: Article
UDC: 519.71
Language: Russian
Citation: E. S. Palamarchuk, “On optimal control in the problem of long-run tracking the exponential Ornstein—Uhlenbeck process”, Sib. Zh. Ind. Mat., 25:4 (2022), 116–135; J. Appl. Industr. Math., 16:4 (2022), 720–736
Citation in format AMSBIB
\Bibitem{Pal22}
\by E.~S.~Palamarchuk
\paper On optimal control in the problem of long-run tracking the exponential Ornstein---Uhlenbeck process
\jour Sib. Zh. Ind. Mat.
\yr 2022
\vol 25
\issue 4
\pages 116--135
\mathnet{http://mi.mathnet.ru/sjim1200}
\transl
\jour J. Appl. Industr. Math.
\yr 2022
\vol 16
\issue 4
\pages 720--736
\crossref{https://doi.org/10.1134/S1990478922040135}
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