Probabilistic approach to the continuous model of exchange in the economy
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- Category: Economy and management
- Last Updated on 04 February 2016
- Published on 04 February 2016
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Authors:
V.M. Kuznichenko, Cand. Sci. (Phys.-Math.), Associate Professor, Kharkiv Institute of Finance of the Ukrainian State University of Finance and International Trade, Senior Lecturer of the Department of Economics and Mathematical Methods and Information Technology, Kharkiv, Ukraine.
V.I. Lapshyn, Dr. Sci. (Phys.-Math.), Professor, Kharkiv Institute of Finance of the Ukrainian State University of Finance and International Trade, Professor of the Department of Economics and Mathematical Methods and Information Technology, Kharkiv, Ukraine.
Abstract:
Purpose. Construction of a deficit-free model of exchange for continuous processes with an external management.
Methodology. Based on the Markov Chain theory, methods of the Laplace transform and 
Findings. The methodology of construction of the deficit-free model of exchange based on the Markov Chain theory for continuous processes with an external management was developed. The results of the continuous and discrete models coincide. A deficit- free model assumes that in the process of exchange and when entering the stationary mode its participants have zero balance. Control force as an action of administration due to the redistribution can correct the results of exchange between the participants of the process. The model allows determining the control force (influence) for the processes of realization of a certain program of exchange.
Originality. Earlier, the deficit-free model of exchange that is based on the Markov Chain theory with an external management was constructed and used only for discrete processes.
Practical value. The model may be used in the different economic systems for the study and planning of exchange processes taking into account an external management continuous in time. Such systems can exemplify the linear model of international trade, money and commodity streams between the performers of regional budgetary projects. Further development of the research supposes the construction of a deficit model. In the deficit model, the processes of receipt and transmission of elements of exchange are divided. This can result in a negative or positive balance of some participants.
References:
1. Жлуктенко В.І. Стохастичні процеси та моделі в економіці, соціології, екології / Жлуктенко В.І, Наконечний С.І., Савіна С.С. – К., 2002. – 226с.
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Kuznichenko, V.M. and Lapshin, V.I. and Stetsenko, T.V. (2014), Stokhasticheskiy podkhod k analizu lineynoy modeli obmena: Primenenie tsepey Markova v reshenii zadach upravleniya ekonomicheskimi sistemami [The Stochastic Approach to the Analysis of a Linear Exchange Model: Application of Markov Chains in the Task of Economic Systems], Monograph, Palmarium Academic Publishing, Saarbrücken, Germany.
4. Гандмахер Ф.Р. Теория матриц: 5-е изд. / Гандмахер Ф.Р. − М.: Физматлит, 2004. – 560с.
Gandmakher, F.R. (2004), Teoriya matrits [Theory of Matrices], 5nd, Moscow, Fizmatlit, Russia.
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