Wyniki wyszukiwania - BazTech

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On the theory elements and methods of parametrical regulation of the national economy evolution based on discrete stochastic dynamic models

Ashimov A. A., Sultanov B. T., Borovskiy Y. V., Novikov D. A., Serovajsky S. Y., Ashimov A. A.

Systems Science

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2010

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Vol. 36, no 4

5-12

EN

The work presents results on development of the parametrical regulation theory for a class of discrete stochastic dynamic systems with additive noise. Within the framework of development of the parametrical regulation theory for discrete dynamic systems we formulated and proved the theorem about sufficient conditions for existence of solutions to the problems of variational calculus on synthesis of optimal laws of parametrical regulation and the theorem about sufficient conditions for continuous dependence of criterions' optimal values of the problem of the values of unregulated parameters. The discrete stochastic model, taken as an example, was obtained from one deterministic computable model of general equilibrium of economic sectors by adding additive noise to the right parts of dynamic equations of the model. The problem of parametrical identification of the deterministic variant of the model was preliminarily solved based on the statistical data for the Republic of Kazakhstan. For the stochastic and deterministic variants of the investigated model problems of optimal economic growth of national economy of the Republic of Kazakhstan were formulated and solved (applying the methods of parametrical regulation theory).

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Parametrical regulation af economic growth on the basis of mathematical model with the account of foreign commerce

Ashimov A. A., Isakov N. A., Borovskiy Y. V., Sultanov B. T., Ashimov A. A.

Systems Science

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2009

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Vol. 35, no 2

101-106

EN

The paper is devoted to the application of the theory of parametrical regulation offered by the authors to tasks of maintenance of economic growth with the account of foreign commerce. In the report the mathematical model of economic system of the country is given in view of specified influence. The factors of the mathematical model considered have been evaluated as a result of solving a task of parametrical identification on the statistical data of national economics of the Republic of Kazakhstan and the Russian Federation. The weak structural stability of the specified mathematical model in a compact of eight-dimensional Euclidean space of the phase variables without parametrical regulation has been proved. The proof is based on results of C. Robinson work about structural stability on manifolds with boundary. The methods of the parametrical regulation theory determine the optimum laws of parametrical regulation of processes of economic growth of the Republic of Kazakhstan. These optimum laws are as extremals of the appropriate of variational calculus task at their choice in environment of the given finite set of algorithms. The specified algorithms represent dependences of these or those parameters of mathematical model on some endogenous variables. The dependences of the found laws on influence of two unguided parameters - interest rates on deposits of bank system of the Republic of Kazakhstan and currency exchange rate are being investigated. These dependences are presented as graphs of the criterion's (gross domestic product) optimal values on the parameters of interest rates on deposits and currency exchange rate. The specified graph determines the set of bifurcation points of this two-dimensional parameter. Also, the weak structural stability of the mathematical model with parametrical regulation has been proved.

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Parametrical regulation methods of the market economy mechanisms

Ashimov A. A., Borovskiy Y. V., Ashimov A. A.

Systems Science

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2005

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Vol. 31, no 1

89-103

EN

The tasks of parametrical regulation of mechanisms of market economy are considered on the basis of two mathematical models of economic systems. The models are described using the systems of the differential and algebraic equations, which can be reduced to systems of the differential equations. The solution and research of systems was carried out using a method of Runge-Kulta. An approach to the choice of effective algorithms in environment of a given set of the laws of regulation as statement and decision of separate extreme tasks at a level one, two and three regulable economic parameters is offered.