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Proceedings Paper

Power-law distributions in economics: a nonextensive statistical approach
Author(s): Silvio M. Duarte Queiros; Celia Anteneodo; Constantino Tsallis
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Paper Abstract

The cornerstone of Boltzmann-Gibbs (BG) statistical mechanics is the Boltzmann-Gibbs-Jaynes-Shannon entropy SBG≡ -k &sh; dx f(x) ln f(x), where k is a positive constant and f(x) a probability density function. This theory has exibited, along more than one century, great success in the treatment of systems where short spatio/temporal correlations dominate. There are, however, anomalous natural and artificial systems that violate the basic requirements for its applicability. Different physical entropies, other than the standard one, appear to be necessary in order to satisfactorily deal with such anomalies. One of such entropies is Sq ≡ k (1-&sh; dx [f(x)]q)=(1-q) (with S1 = SBG), where the entropic index q is a real parameter. It has been proposed as the basis for a generalization, referred to as nonextensive statistical mechanics, of the BG theory. Sq shares with SBG four remarkable properties, namely concavity (8q > 0), Lesche-stability (8q > 0), finiteness of the entropy production per unit time (q 2 <), and additivity (for at least a compact support of q including q = 1). The simultaneous validity of these properties suggests that Sq is appropriate for bridging, at a macroscopic level, with classical thermodynamics itself. In the same natural way that exponential probability functions arise in the standard context, power-law tailed distributions, even with exponents out of the Levy range, arise in the nonextensive framework. In this review, we intend to show that many processes of interest in economy, for which fat-tailed probability functions are empirically observed, can be described in terms of the statistical mechanisms that underly the nonextensive theory.

Paper Details

Date Published: 23 May 2005
PDF: 14 pages
Proc. SPIE 5848, Noise and Fluctuations in Econophysics and Finance, (23 May 2005); doi: 10.1117/12.619469
Show Author Affiliations
Silvio M. Duarte Queiros, Ctr. Brasileiro de Pesquisas Fisicas (Brazil)
Celia Anteneodo, Pontificia Univ. Catolica do Rio de Janeiro (Brazil)
Constantino Tsallis, Ctr. Brasileiro de Pesquisas Fisicas (Brazil)
Santa Fe Institute (United States)

Published in SPIE Proceedings Vol. 5848:
Noise and Fluctuations in Econophysics and Finance
Derek Abbott; Jean-Philippe Bouchaud; Xavier Gabaix; Joseph L. McCauley, Editor(s)

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