Informatics and Applications
2021, Volume 15, Issue 4, pp 3340
CREATION OF A STOCHASTIC DYNAMIC ONESECTOR ECONOMIC MODEL WITH DISCRETE TIME AND ANALYSIS OF THE CORRESPONDING OPTIMAL CONTROL PROBLEM
Abstract
The work is devoted to the creation of a stochastic dynamic model of optimal control with discrete time within the framework of a onesector economic system. The basis is a classical deterministic dynamic model of the economic system in which one universal product is produced. This product is divided into investment and consumer components. System management consists in determining the relationship between these components.
In this work, it is assumed that the main parameters of the system depend on some random factor that characterizes the influence of the external environment. This factor is described by a homogeneous Markov chain with a finite set of states and a given transition probability matrix. In this work, a stochastic model of the evolution of the system under consideration is constructed which is a twodimensional Markov process with discrete time. In terms of its economic content, the first component of this process is specific capital and the second is the state of an external random factor. The control parameter or decision at each moment of time represents the share of the specific product produced directed to investment. The recurrent setting of the cost additive indicator of management efficiency is described. The theoretical basis for solving the problem of optimal control is the method of dynamic programming. In this work, a system of Bellman functional equations is obtained, the solution of which is the optimal control strategy.
[+] References (13)
 Ashmanov, S. A. 1980. Matematicheskie modeli i metody v ekonomike [Mathematical models and methods in economics]. Moscow: Moscow University Press. 199 p.
 Intriligator, M. 2002. Mathematical methods of optimization and economic theory. Philadelphia, PA: SIAM. 508 p.
 Ioffe, A. D., and V. M. Tikhomirov. 1974. Teoriya ekstremal'nykh zadach [Extremal problems theory]. Moscow: Nauka. 480 p.
 Livshits, K.I., and Yu. I. Paraev. 2020. Optimal'noe upravlenie [Optimal control]. St. Petersburg: Lan'. 232 p.
 Kamien, M., and N. Schwartz. 1981. Dynamic optimization. New York, NY: Elsevier North Holland. 331 p.
 Barro, R., and X. SalaiMartin. 2004. Economic growth. 2nd ed. Cambridge, MA: MIT Press. 654 p.
 Paraev, Yu. I. 2015. Optimal'noe upravlenie v dinamicheskoy economike [Optimal control in a dynamic economy]. Tomsk: NTL. 104 p.
 Shnurkov, P. V., and A. O. Rudak. 2019. Algoritmicheskoe reshenie problemy optimal'nogo upravleniya v dinamicheskoy odnosektornoy ekonomicheskoy modeli na osnove metoda dinamicheskogo programmirovaniya [Algorithmic solution of the problem of optimal control in a dynamic onesector economic model based on the method of dynamic programming]. Sistemy i Sredstva In formatiki  Systems and Means of Informatics 29(1):128 139.
 Shiryaev, A. N. 2019. Probability2. Graduate texts in mathematics ser. 3rded. New York, NY: Springer. Vol. 95. 358 p.
 Bellman, R. 1972. Dynamic programming. 6th ed. Princeton, NJ: Princeton University Press. 402 p.
 Bellman, R., and S. Dreyfus. 1962. Applied dynamic programming. London: Oxford University Press. 363 p.
 Howard, R. A. 1960. Dynamic programming and Markov processes. Cambridge, MA: MIT Press. 136 p.
 Mine, H., and S. Osaki. 1970. Markovian decision processes. New York, NY: Elsevier. 142 p.
[+] About this article
Title
CREATION OF A STOCHASTIC DYNAMIC ONESECTOR ECONOMIC MODEL WITH DISCRETE TIME AND ANALYSIS OF THE CORRESPONDING OPTIMAL CONTROL PROBLEM
Journal
Informatics and Applications
2021, Volume 15, Issue 4, pp 3340
Cover Date
20211230
DOI
10.14357/19922264210405
Print ISSN
19922264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
optimal control problem with discrete time; stochastic dynamic onesector economic model; controlled twodimensional Markov chain; dynamic programming method for a discretetime control problem; Bellman equations
Authors
P. V. Shnurkov
Author Affiliations
National Research University Higher School of Economics, 34 Tallinskaya Str., Moscow 123458, Russian Federation
