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Power laws of wealth, market order volumes and market returns

  • Solomon, Sorin
  • Richmond, Peter
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    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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    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
    Contact details of provider: Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

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    1. Parameswaran Gopikrishnan & Vasiliki Plerou & Xavier Gabaix & H. Eugene Stanley, 2000. "Statistical Properties of Share Volume Traded in Financial Markets," Papers cond-mat/0008113, arXiv.org.
    2. Zhi-Feng Huang, Sorin Solomon*, 2001. "Power, Levy, Exponential and Gaussian Regimes in Autocatalytic Financial Systems," Computing in Economics and Finance 2001 12, Society for Computational Economics.
    3. Sorin Solomon & Peter Richmond, 2000. "Stability of Pareto-Zipf Law in Non-Stationary Economies," Papers cond-mat/0012479, arXiv.org, revised Jan 2001.
    4. Levy, Moshe & Solomon, Sorin, 1997. "New evidence for the power-law distribution of wealth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 242(1), pages 90-94.
    5. Sergei Maslov & Mark Mills, 2001. "Price fluctuations from the order book perspective - empirical facts and a simple model," Papers cond-mat/0102518, arXiv.org.
    6. Maslov, Sergei & Mills, Mark, 2001. "Price fluctuations from the order book perspective—empirical facts and a simple model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 234-246.
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