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Category: Economy and management

Last Updated on 17 November 2017

Published on 17 November 2017

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Authors:

V.M.Kuznichenko, Cand. Sc. (Phys.-Math.), Assoc. Prof., National University of Trade and Economics, Kharkiv Institute of Finance, Associate Professor of the Department of Economics and Mathematical Methods and Information Technology, Kharkiv, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

V.I.Lapshyn, Dr. Sc. (Phys.-Math.), Prof., National University of Trade and Economics, Kharkiv Institute of Finance, Professor of the Department of Economics and Mathematical Methods and Information Technology, Kharkiv, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Abstract:

Purpose. A method for constructing a deficit-having model of exchange based on the Markov chain theory for continuous processes with an external management is demonstrated. The results of the continuous and discrete models are identical at the moments of time proportional to the time step of discrete process.

Methodology. The Markov Chain theory, method of Z ‒ transformation are used for determining vectors of the supply and demand between those taking part in the exchange processes. The intensity matrices are defined from transformation of logarithmic function of corresponding transition matrices into polynomials. This is done with help of the Cayley-Hamilton theorem.

Findings. The developed deficit-having model of exchange is investigated. The method of constructing a deficit-having model of exchange is demonstrated on the example. The discrete model is used for constructing the continuous model. The vectors of the supply and demand in the exchange process are determined.

Originality. Previously the method for constructing a deficit-having model of exchange on the basis of the Markov Chain theory for continuous processes with an external management was presented briefly without examples. On the example of three partners of exchange process the transition from the deficit-free model to the deficit-having one is shown.

Practical value. The continuous model can be used in different economic systems for studying and planning exchange processes. Such systems can be exemplified by a linear model of international trade, money and commodity streams between the performers of regional budgetary projects. The developed model of exchange allows us to analyse separately the supply and demand between partners, to determine the balance of the exchange process, and increases the management level. At further development the built model of exchange can be used for the queuing systems with an external management.

References:

1. Zhuktenko, V. I. and Begun, A. V., 2005. Stochastic models in economics. Kiev: KNEU.

2. Sokolov, G. A. and Chistiakov, N. A., 2005. Probability. Controlled Markov Chains in the economy. Moscow.

3. Kuznichenko, V. M. and Lapshyn, V. I., 2015. Probabilistic approach to the continuous model in the economy. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, 5, рр. 137‒141.

4. Kostenko, E., Kuznichenko, V. M. and Lapshyn, V. I., 2016. Deficit model of exchange for continuous processes with external control, Applied Economics Letters [e-journal]. pp. 1‒4. doi: 10.1080/13504851.2016.1205717.

5. Gandmakher, F. R., 2010. Theory of matrices. Moscow: Fizmatlit. 

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2017-11-15  1.59 MB  731

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