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Power laws of wealth, market order volumes and market returns

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  • Solomon, Sorin
  • Richmond, Peter
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    Abstract

    Using the Generalized Lotka Volterra model adapted to deal with mutiagent systems we can investigate economic systems from a general viewpoint and obtain generic features common to most economies. Assuming only weak generic assumptions on capital dynamics, we are able to obtain very specific predictions for the distribution of social wealth. First, we show that in a ‘fair’ market, the wealth distribution among individual investors fulfills a power law. We then argue that ‘fair play’ for capital and minimal socio-biological needs of the humans traps the economy within a power law wealth distribution with a particular Pareto exponent α∼32. In particular, we relate it to the average number of individuals L depending on the average wealth: α∼L/(L−1). Then we connect it to certain power exponents characterizing the stock markets. We find that the distribution of volumes of the individual (buy and sell) orders follows a power law with similar exponent β∼α∼32. Consequently, in a market where trades take place by matching pairs of such sell and buy orders, the corresponding exponent for the market returns is expected to be of order γ∼2α∼3. These results are consistent with recent experimental measurements of these power law exponents (S. Maslov, M. Mills, Physica A 299 (2001) 234 for β; P. Gopikrishnan et al., Phys. Rev. E 60 (1999) 5305 for γ).

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    File URL: http://www.sciencedirect.com/science/article/pii/S0378437101002953
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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 299 (2001)
    Issue (Month): 1 ()
    Pages: 188-197

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    Handle: RePEc:eee:phsmap:v:299:y:2001:i:1:p:188-197

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Pareto–Zipf; Random multiplicative process; Wealth distribution; Market returns;

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    Cited by:
    1. Victor M. Yakovenko, 2007. "Econophysics, Statistical Mechanics Approach to," Papers 0709.3662, arXiv.org, revised Aug 2008.
    2. David Morton de Lachapelle & Damien Challet, 2009. "Turnover, account value and diversification of real traders: evidence of collective portfolio optimizing behavior," Papers 0912.4723, arXiv.org, revised Jun 2010.
    3. Emeterio Navarro & Ruben Cantero & Joao Rodrigues & Frank Schweitzer, 2007. "Investments in Random Environments," Papers 0709.3630, arXiv.org, revised Sep 2008.
    4. Ari Belenkiy, 2001. "Inner Market as a "Black Box"," Papers cond-mat/0106401, arXiv.org.
    5. G. Yaari & D. Stauffer & S. Solomon, 2008. "Intermittency and Localization," Papers 0802.3541, arXiv.org, revised Mar 2008.
    6. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.

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