scholarly journals On History of Mathematical Economics: Application of Fractional Calculus

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 509 ◽  
Author(s):  
Vasily Tarasov
Keyword(s):  
Economic Theory ◽  
Fractional Calculus ◽  
Deterministic Chaos ◽  
Present Moment ◽  
Mathematical Tool ◽  
Integral Calculus ◽  
Mathematical Economics ◽  
Economic Agents ◽  
History Of ◽  
Modern Economic

Modern economics was born in the Marginal revolution and the Keynesian revolution. These revolutions led to the emergence of fundamental concepts and methods in economic theory, which allow the use of differential and integral calculus to describe economic phenomena, effects, and processes. At the present moment the new revolution, which can be called “Memory revolution”, is actually taking place in modern economics. This revolution is intended to “cure amnesia” of modern economic theory, which is caused by the use of differential and integral operators of integer orders. In economics, the description of economic processes should take into account that the behavior of economic agents may depend on the history of previous changes in economy. The main mathematical tool designed to “cure amnesia” in economics is fractional calculus that is a theory of integrals, derivatives, sums, and differences of non-integer orders. This paper contains a brief review of the history of applications of fractional calculus in modern mathematical economics and economic theory. The first stage of the Memory Revolution in economics is associated with the works published in 1966 and 1980 by Clive W. J. Granger, who received the Nobel Memorial Prize in Economic Sciences in 2003. We divide the history of the application of fractional calculus in economics into the following five stages of development (approaches): ARFIMA; fractional Brownian motion; econophysics; deterministic chaos; mathematical economics. The modern stage (mathematical economics) of the Memory revolution is intended to include in the modern economic theory new economic concepts and notions that allow us to take into account the presence of memory in economic processes. The current stage actually absorbs the Granger approach based on ARFIMA models that used only the Granger–Joyeux–Hosking fractional differencing and integrating, which really are the well-known Grunwald–Letnikov fractional differences. The modern stage can also absorb other approaches by formulation of new economic notions, concepts, effects, phenomena, and principles. Some comments on possible future directions for development of the fractional mathematical economics are proposed.

B is for Bias

2014 ◽  
Vol 3 (2) ◽  
pp. 35-47
Author(s):  
Calin Valsan
Keyword(s):  
Economic Theory ◽  
Rational Expectations ◽  
Economic Environment ◽  
Rational Agents ◽  
Economic Agents ◽  
Behavioral Biases ◽  
The Social ◽  
Modern Economic

Standard economic theory assumes rational agents. Individuals are expected to have rational expectations and constantly optimize their choices. Modern economic and financial theory is build under the assumption of rationality. There is plenty of evidence from psychology, however, that individuals are biased and rely heavily on heuristics in order to make decisions. Yet, this is not a mere fluke, a behavioral oddity. Because the social and economic environment in which individuals evolve is complex, behavioral biases represent evolutionary adaptations allowing economic agents to deal with undecidability and computational irreducibility.

scholarly journals Retrospectives: What Did the Ancient Greeks Mean by Oikonomia?

2016 ◽  
Vol 30 (1) ◽  
pp. 225-238 ◽  
Author(s):  
Dotan Leshem
Keyword(s):  
Economic Theory ◽  
Economic Thought ◽  
Short History ◽  
Ancient Greek ◽  
Active Participant ◽  
Economic Action ◽  
History Of ◽  
Modern Economic ◽  
City State ◽  
The City

Nearly every economist has at some point in the standard coursework been exposed to a brief explanation that the origin of the word “economy” can be traced back to the Greek word oikonomia, which in turn is composed of two words: oikos, which is usually translated as “household”; and nemein, which is best translated as “management and dispensation.” Thus, the cursory story usually goes, the term oikonomia referred to “household management” and while this was in some loose way linked to the idea of budgeting, it has little or no relevance to contemporary economics. This article introduces in more detail what the ancient Greek philosophers meant by “oikonomia.” It begins with a short history of the word. It then explores some of the key elements of oikonomia, while offering some comparisons and contrasts with modern economic thought. For example, both Ancient Greek oikonomia and contemporary economics study human behavior as a relationship between ends and means which have alternative uses. However, while both approaches hold that the rationality of any economic action is dependent on the frugal use of means, contemporary economics is largely neutral between ends, while in ancient economic theory, an action is considered economically rational only when taken towards a praiseworthy end. Moreover, the ancient philosophers had a distinct view of what constituted such an end—specifically, acting as a philosopher or as an active participant in the life of the city-state.

Epistemological aspects of self-organization processes in socio-economic systems from the standpoint of economic and mathematical modeling

2019 ◽  
Author(s):  
Михаил Куссый ◽  
Mihail Kussyy
Keyword(s):  
Mathematical Modeling ◽  
Economic Theory ◽  
Self Organization ◽  
Economic Systems ◽  
Anthropogenic Factor ◽  
Economic Agents ◽  
Existing Problems ◽  
Modern Economic

The monograph examines the processes of self-organization in socio-economic systems and some of their epistemological aspects from the standpoint of economic and mathematical modeling. The existing problems of modern economic theory, as well as approaches to modern research in economics, are investigated. It is shown that the key role in the processes of self-organization in socio-economic systems is played by the anthropogenic factor (namely, the expectations and preferences of economic agents). The main characteristics and mechanisms of self-organization processes in socio-economic systems, as well as the reasons that determine them, are investigated. The actual problems of mathematical modeling in economics are noted and solutions to some of these problems are proposed. It is recommended to researchers dealing with the problems of socio-economic systems behavior and its modeling.

The Use of Mathematics in Economics

2006 ◽  
pp. 53-72
Author(s):  
S. Dow
Keyword(s):  
Mathematical Modeling ◽  
Economic Theory ◽  
Economic Science ◽  
Mathematical Research ◽  
Methodological Issues ◽  
Mathematical Methods ◽  
History Of ◽  
Modern Economic

The article examines the history of mathematical methods in economic science and their impact on the structure and factors of development of the modern economic theory. The author considers different features of mathematical modeling in it, giving some examples and analyzing theoretical and methodological issues arising in the process of economic and mathematical research.

The Symbiosis of Economic Science and Practice in Reforming (On the Book by S. Ya. Chernavsky “Reforms of the Energy Regulated Branches in Russia”)

2014 ◽  
pp. 114-124
Author(s):  
V. Makarov
Keyword(s):  
Mathematical Modeling ◽  
Economic Theory ◽  
Mathematical Models ◽  
Economic Science ◽  
Successful Implementation ◽  
Policy Recommendations ◽  
Economic Agents ◽  
Modern Economic ◽  
Econometrics Analysis

The book by S. Chernavsky is devoted to the reform of the Russian energy sector and the economy as a whole. The author assesses in detail carried out reforms and develops policy recommendations in the interest of the society. In some chapters of this book the author plays the role of an analyst, in the others - that of one of the participants directly involved in the reform or its main developer. In all cases, the analysis is combined with the use of modern economic theory, mathematical models of the behavior of economic agents and empirical data. Many mathematical models presented have been developed and evaluated in cooperation with the leading Russian experts in the field of mathematical modeling and econometrics analysis that determines their validity. The obtained results and policy recommendations allow us to count on lower transformation costs and higher probability of successful implementation of reforms.

Methodological Principles of Keynes’ Theory and His «Strife over Method» with Tinbergen

2007 ◽  
pp. 25-36 ◽  
Author(s):  
I. Rozmainsky
Keyword(s):  
Economic Theory ◽  
Critical View ◽  
Modern Economic ◽  
Methodological Principles

The author analyzes Keynes-Tinbergen controversy in the context of Keynes’ methodological ideas, which he thinks are fully opposite to the methodology of modern economic theory. Using different Keynes’ papers the author considers this difference in detail and shows its links to the critical view held by Keynes towards econometrics

Nikolay Sieber in the history of prerevolutionary Russian economic thought

2018 ◽  
pp. 95-110
Author(s):  
L. D. Shirokorad
Keyword(s):  
Economic Theory ◽  
Political Economy ◽  
Organic Synthesis ◽  
Marginal Utility ◽  
Economic Thought ◽  
History Of ◽  
Three Stages

This article shows how representatives of various theoretical currents in economics at different times in history interpreted the efforts of Nikolay Sieber in defending and developing Marxian economic theory and assessed his legacy and role in forming the Marxist school in Russian political economy. The article defines three stages in this process: publication of Sieber’s work dedicated to the analysis of the first volume of Marx’s Das Kapital and criticism of it by Russian opponents of Marxian economic theory; assessment of Sieber’s work by the narodniks, “Legal Marxists”, Georgiy Plekhanov, and Vladimir Lenin; the decline in interest in Sieber in light of the growing tendency towards an “organic synthesis” of the theory of marginal utility and the Marxist social viewpoint.

Beyond GDP: The Quest for a Measure of Social Welfare. Part I

2012 ◽  
pp. 67-93 ◽  
Author(s):  
M. Fleurbaey
Keyword(s):  
Economic Theory ◽  
Social Welfare ◽  
Well Being ◽  
National Product ◽  
Future Generations ◽  
Modern Economic ◽  
Aggregate Wealth ◽  
Net National Product ◽  
Sustainability Policy ◽  
Beyond Gdp

The first part of the paper is devoted to the monetary indicators of social welfare. It is shown which methods of quantitative estimating the aggregate wealth and well-being are available in the modern economic theory apart from the traditional GDP measure. The limitations of the methods are also discussed. The author shows which measures of welfare are adequate in the dynamic context: he considers the problems of intertemporal welfare analysis using the Net National Product (NNP) for the sustainability policy and in the context of concern for well-being of the future generations.

Essays of a “comparatively progressive” economist (On the 150th birth anniversary of Vladimir Geleznoff)

2019 ◽  
pp. 135-145
Author(s):  
Viktor A. Popov
Keyword(s):  
Economic Theory ◽  
Political Economy ◽  
Economic Thought ◽  
History Of Economic Thought ◽  
The Political ◽  
Russian History ◽  
Working Ability ◽  
Intellectual Inquiry ◽  
History Of

Deep comprehension of the advanced economic theory, the talent of lecturer enforced by the outstanding working ability forwarded Vladimir Geleznoff scarcely at the end of his thirties to prepare the publication of “The essays of the political economy” (1898). The subsequent publishing success (8 editions in Russia, the 1918­-year edition in Germany) sufficiently demonstrates that Geleznoff well succeded in meeting the intellectual inquiry of the cross­road epoch of the Russian history and by that taking the worthful place in the history of economic thought in Russia. Being an acknowledged historian of science V. Geleznoff was the first and up to now one of the few to demonstrate the worldwide community of economists the theoretically saturated view of Russian economic thought in its most fruitful period (end of XIX — first quarter of XX century).

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