Informatics and Applications
2024, Volume 18, Issue 3, pp 80-88
NUMERICAL-ANALYTICAL SOLUTION OF THE DISCRETE-TIME TUNING PROBLEM FOR AN INTERVENTION MODEL IN THE FOREIGN EXCHANGE MARKET
- P. V. Shnurkov
- D. A. Novikov
Abstract
The work examines the problem of optimizing external influences (controls) on the process of changing
the price of the so-called bi-currency basket on the foreign exchange market of the Russian Federation. The
theoretical basis of the approach used is the solution of a stochastic tuning problem with discrete time. Based on
the previous statistical analysis, it was established that the stochastic process characterizing the evolution of the
bi-currency basket price, under certain conditions, can be quite adequately described by a classical homogeneous
Markov chain. In this case, statistical estimates of the transition probabilities of the specified chain were obtained.
Necessary auxiliary probabilistic characteristics of the Markov model are numerically determined. For various
given cost characteristics, a study of the stationary cost indicator of management efficiency-average specific profit
was conducted. Specific numerical solutions to the corresponding optimal control problem are obtained which can
be interpreted as optimal external influences (interventions) on the stochastic process under study.
[+] References (6)
- Shnurkov, P. V. 2017. Optimal control problem in a stochastic
model with periodic hits on the boundary of a given
subset of the state set (tuning problem). Cornell University.
16 p. Available at: https://arxiv.org/abs/1709.03442v1
(accessed July 29, 2024).
- Shnurkov, P. V. 2016. Solution of the unconditional extremum
problem for a linear-fractional integral functional
on a set of probability measures. Dokl. Math.
94(2):550–554. doi: 10.1134/S1064562416050161. EDN:
XFUJKH.
- Shnurkov, P. V., A.K. Gorshenin, and V. V. Belousov. 2016.
Analiticheskoe reshenie zadachi optimal’nogo upravleniya
polumarkovskim protsessom s konechnym mnozhestvom
sostoyaniy [Analytical solution of the optimal control task
of a semi-Markov process with finite set of states]. Informatika
i ee Primeneniya — Inform. Appl. 10(4):72–88. doi:
10.14357/19922264160408. EDN: XGSITZ.
- Shnurkov, P. V., and D.A. Novikov. 2018. Analysis of the
problem of intervention control in the economy on the basis
of solving the problem of tuning. Cornell University. 15 p.
Available at: https://arxiv.org/abs/1811.10993 (accessed
July 29, 2024).
- Shnurkov, P. V., and D. A. Novikov. 2020. O kontseptsii
stokhasticheskoy modeli s upravleniem v momenty vykhoda
protsessa na granitsu zadannogo podmnozhestva mnozhestva
sostoyaniy [On the concept of a stochastic model
with control at the moments of the process at the border
of a presented subset of multiple states]. Informatika
i ee Primeneniya — Inform. Appl. 14(3):101–108. doi:
10.14357/19922264200315. EDN: FSLGBJ.
- Shnurkov, P. V., and M.A. Migulya. 2022. Nekotorye rezul’taty
analiza protsessa izmeneniya tseny bivalyutnoy korziny
na osnove metodov statistiki sluchaynykh protsessov
[Some results of the analysis of the process of changing the
price of a dual currency basket based on random process
statistics methods]. Informatika i ee Primeneniya— Inform.
Appl. 16(3):16–25. doi: 10.14357/19922264220303. EDN: QGZCHT
[+] About this article
Title
NUMERICAL-ANALYTICAL SOLUTION OF THE DISCRETE-TIME TUNING PROBLEM FOR AN INTERVENTION MODEL IN THE FOREIGN EXCHANGE MARKET
Journal
Informatics and Applications
2024, Volume 18, Issue 3, pp 80-88
Cover Date
2024-09-20
DOI
10.14357/19922264240310
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
stochastic Markov and semi-Markov control models; discrete time tuning problem; fractional linear integral functionals on discrete probability distributions; optimal control in stochastic economic systems
Authors
P. V. Shnurkov  and D. A. Novikov
Author Affiliations
National Research University “Higher School of Economics,” 34 Tallinskaya Str., Moscow 123458, Russian Federation
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