What is it about?

In monograph [A. Ashimov, B.T. Sultanov, Zh.M. Adilov, Yu.V. Borovskiy, D.A. Novikov, R.A. Alshanov, As.A. Ashimov, Macroeconomic analysis and parametrical control of a national economy (New York: Springer, 2013)] it is described the proposed theory of parametric control of the national economy on the basis of deterministic continuous dynamic models, deterministic discrete dynamical models of stochastic discrete dynamical models with additive noise. The theory consists of 8 components, in which: - proposed applied approach for evaluating the structural stability and mathematical models sustainability indicators for the assessment of conditions for transferring of computational experiments results to the respective subject areas; - formulated and proved theorems on conditions of existence of variational calculus problem on the synthesis and the choice of optimal laws of parametrical regulation; - proposed a method of investigating of results dependence of considered variations calculus problems from the variations of unregulated parameters. In particular, it defines the point of bifurcation extremals of variational calculus tasks on the choice of optimal laws of parametrical regulation, formulated and proved a theorem about the conditions of this bifurcation point existence. The efficiency of the parametric control theory is illustrated by a number of examples, which include: mathematical model of the neoclassical theory of optimal growth, mathematical model of the economic system of the country, taking into account the effect of the proportions of State spending and the rate of interest on government loans for economic growth, mathematical model of the economic system of the country, taking into account the impact of international trade and currency exchanges on economic growth, Turnovsky monetary model, Jones endogenous model, computable general equilibrium model of economic sectors, Forrester mathematical model of the global economy and others.

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Why is it important?

The importance of the evaluation results of conditions for transferring of the results of computational experiments on mathematical models to the relevant subject areas is underlined by the absence in well-known literature. The proposed methods of synthesis and the choice of parametrical regulation laws are differ from well-known results on the study of parametric disturbances like [Ioffe A.D., Tihomirov V.M. The Theory of Extremal Problems. Moscow: Nauka, 1974.], where parametric perturbation is applied to obtain sufficient extremum conditions by plotting the corresponding S-functions and applying the principle dropping of restrictions, or [Ulam S. Unsolved Mathematical Problems. Moscow: Nauka, 1964. (in Russian)] where questioned is set about the conditions of stability of variational calculus problems solving (Ulama’s problem). Therefore they have applied relevance for the solution to the corresponding problems of variational calculus on mathematical models of macroeconomic systems belonging to the classes of econometric models, conjunctural cycles models and computable models of general equilibrium.

Perspectives

Demonstrated effectiveness of the proposed evaluation methods of conditions for transferring of obtained results of computational experiments on mathematical models to the respective subject areas and synthesis methods and the choice of parametrical regulation laws show that this monograph can be considered as a development of modern macroeconomic theory, and the proposed methods applied to solve relevant problems of macroeconomic practice.

Abdykappar Ashimov
Kazakh National Technical University

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This page is a summary of: Conclusion, January 2012, Springer Science + Business Media,
DOI: 10.1007/978-1-4614-4460-2_5.
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