E. S. Palamarchuk, “On optimal control in the problem of long-run tracking the exponential Ornstein—Uhlenbeck process ”, Sib. Zh. Ind. Mat., 2022, Volume 25, Number 4,Pages <nobr>116

On optimal control in the problem of long-run tracking the exponential Ornstein—Uhlenbeck process

E. S. Palamarchuk^ab

^a Central Economics and Mathematics Institite RAS, Nakhimovsky prosp. 47, Moscow 117418, Russia
^b Higher School of Economics, Pokrovsky bul. 11, Moscow 109028, Russia

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. .

UDC: 519.71

Received: 11.04.2022
Revised: 16.06.2022
Accepted: 22.06.2022

DOI: 10.33048/SIBJIM.2021.25.410