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JOURNALS // Avtomatika i Telemekhanika // Archive

Avtomat. i Telemekh., 2019 Issue 8, Pages 64–75 (Mi at15316)

This article is cited in 3 papers

Control in Technical Systems

Optimal control problems with disorder

G. I. Belyavskiiab, N. V. Danilovaab, I. A. Zemlyakovaab

a Vorovich Institute of Mathematics, Mechanics, and Computer Science, Rostov-on-Don, Russia
b Southern Federal University, Rostov-on-Don, Russia

Abstract: We consider a generalization of processes with disorder, namely processes with a vector disorder. For these problems, we consider a class of optimal control problems that do not detect the disorder. We propose a computational method for solving control problems on a finite time interval and with an objective functional defined at the end of the interval, based on the use of the martingale technique. We consider a computational experiment for a model with two barriers and two stopping times.

Keywords: processes with disorder, vector disorder, martingale, martingale measure, Wiener process, quantile hedging.


Received: 23.10.2018
Revised: 23.02.2019
Accepted: 25.04.2019

DOI: 10.1134/S0005231019080063


 English version:
Automation and Remote Control, 2019, 80:8, 1419–1427

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© Steklov Math. Inst. of RAS, 2024