Abdykappar A. Ashimov - Böcker

After the transition to free economy, governments of the former Soviet republics realized that in spite of becoming a part of the shaky international economic order, their individual economic success can be assured by rational national economic policies that in addition to the fundamental law of supply and demand govern the economic mechanism sensitive to both external and internal phenomena.  Originally published in Russian and now translated in English, this book by Dr. A. Ashimov and his colleagues offers a novel theory providing a numerically-justifiable approach to the solution of major economy control problems that are faced by virtually every government in the world. First, they developed and validated numerous mathematical models describing complex interactions between economic and social factors thus enabling the decision makers to foresee the outcomes of their decisions. Second, on the basis of these models the authors formulated the appropriate control problems that could be interpreted as achieving the transition to the desirable economic regimes and maintaining these regimes in spite of initial conditions and both external and internal perturbations. It should be noted that due to the inherent uncertainty introduced by the use of statistical models, the nonlinearity of the underlying phenomena and the intention to obtain the optimal solutions, the solution process becomes quite intricate and calls for the application of the most sophisticated techniques offered in advanced control theory. The authors utilized the most instrumental statistical model validation techniques; they established sufficient conditions for the existence of optimal solutions of the relevant control problems; and they skillfully combined the applications of the phase space formalism, system stability analysis, and the methods of functional analysis. Finally, they developed algorithms resulting in the optimal problem solutions, thus offering economic policy makersa dependable decision support tool. Macroeconomic Analysis and Economic Policy Based on Parametric Control offers a novel, highly mathematical approach to the solution of very realistic economy control problems. It presents a good example of the application of mathematical modeling, advanced control theory, and model-based decision making that could be adopted by researchers and graduate students specializing in economics, control, and relevant areas of research, addressing their own research problems.

​​​​​This is a sequel to the book by Dr. A. Ashimov and his colleagues, Macroeconomic Analysis and Economic Policy Based on Parametric Control. The authors have expanded both the developed mathematical apparatus and the scope of problems and applications stemming from the practice of steering a national economy of a small country in the dynamic environment of the international economic order. The developed theoretical foundation is used in Chapter 1 to suggest a decision support system operating in the framework of state economic policy making. Chapter 2 presents various mathematical models built on the basis of the available statistical data and provides quality assessment of these models. Parametric control problems are being formulated on the basis of these models as problems of mathematical programming, and the obtained solutions are subjected to analyses and interpretations. This is demonstrated by the analysis of the effect of uncontrollable factors on the problem solutions. Chapter 3 is aimed at the modelling and analysis of cyclic phenomena in economics and their structural stability. Chapter 4 presents solutions of specific problems of national economy and analysis and interpretation of their solutions. In summary, the authors formulate comprehensive mathematical models of some critical mechanisms in micro economics previously known only on a qualitative level. They provide vigorous mathematical analysis of the models that justifies their applicability for the formulation of parametric control problems, and the existence of model-based solutions. The complexity of the resultant problems is addressed by the formulation of the appropriate algorithms. The described methodology leads to the development of computer-based decision support systems.​

After the transition to free economy, governments of the former Soviet republics realized that in spite of becoming a part of the shaky international economic order, their individual economic success can be assured by rational national economic policies that in addition to the fundamental law of supply and demand govern the economic mechanism sensitive to both external and internal phenomena.  Originally published in Russian and now translated in English, this book by Dr. A. Ashimov and his colleagues offers a novel theory providing a numerically-justifiable approach to the solution of major economy control problems that are faced by virtually every government in the world. First, they developed and validated numerous mathematical models describing complex interactions between economic and social factors thus enabling the decision makers to foresee the outcomes of their decisions. Second, on the basis of these models the authors formulated the appropriate control problems that could be interpreted as achieving the transition to the desirable economic regimes and maintaining these regimes in spite of initial conditions and both external and internal perturbations. It should be noted that due to the inherent uncertainty introduced by the use of statistical models, the nonlinearity of the underlying phenomena and the intention to obtain the optimal solutions, the solution process becomes quite intricate and calls for the application of the most sophisticated techniques offered in advanced control theory. The authors utilized the most instrumental statistical model validation techniques; they established sufficient conditions for the existence of optimal solutions of the relevant control problems; and they skillfully combined the applications of the phase space formalism, system stability analysis, and the methods of functional analysis. Finally, they developed algorithms resulting in the optimal problem solutions, thus offering economic policy makersa dependable decision support tool. Macroeconomic Analysis and Economic Policy Based on Parametric Control offers a novel, highly mathematical approach to the solution of very realistic economy control problems. It presents a good example of the application of mathematical modeling, advanced control theory, and model-based decision making that could be adopted by researchers and graduate students specializing in economics, control, and relevant areas of research, addressing their own research problems.

​​​​​This is a sequel to the book by Dr. A. Ashimov and his colleagues, Macroeconomic Analysis and Economic Policy Based on Parametric Control. The authors have expanded both the developed mathematical apparatus and the scope of problems and applications stemming from the practice of steering a national economy of a small country in the dynamic environment of the international economic order. The developed theoretical foundation is used in Chapter 1 to suggest a decision support system operating in the framework of state economic policy making. Chapter 2 presents various mathematical models built on the basis of the available statistical data and provides quality assessment of these models. Parametric control problems are being formulated on the basis of these models as problems of mathematical programming, and the obtained solutions are subjected to analyses and interpretations. This is demonstrated by the analysis of the effect of uncontrollable factors on the problem solutions. Chapter 3 is aimed at the modelling and analysis of cyclic phenomena in economics and their structural stability. Chapter 4 presents solutions of specific problems of national economy and analysis and interpretation of their solutions. In summary, the authors formulate comprehensive mathematical models of some critical mechanisms in micro economics previously known only on a qualitative level. They provide vigorous mathematical analysis of the models that justifies their applicability for the formulation of parametric control problems, and the existence of model-based solutions. The complexity of the resultant problems is addressed by the formulation of the appropriate algorithms. The described methodology leads to the development of computer-based decision support systems.​

This book is a further development of the theory of parametric control. It includes: numerical methods of testing (verification) of software implementation of mathematical models by assessing the stability of mappings defined by the model; sufficient conditions for the existence of the solutions of some types of problems of dynamic optimization; the existence of continuous dependence of optimal values of criteria on exogenous functions and parameters; and the existence of points of bifurcation of extremals of such problems. It demonstrates that this theory offers a constructive methodology for middle-term forecasting, macroeconomic analysis and estimation of optimal values of economic characteristics on the basis of advanced global mathematical models, namely Computable General Equilibrium (CGE) Model, Dynamic Stochastic General Equilibrium (DSGE) Model, and Hybrid Econometric model. In addition, it includes conditions for the applicability of the computational experiments’ results, into practice.