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Power Laws of Wealth, Market Order Volumes and Market Returns

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  • Sorin Solomon
  • Peter Richmond

Abstract

Using the Generalised Lotka Volterra (GLV) model adapted to deal with muti agent 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 $\alpha \sim 3/2$. In particular we relate it to the average number of individuals L depending on the average wealth: $\alpha \sim L/(L-1)$. Then we connect it to certain power exponents characterising the stock markets. We obtain that the distribution of volumes of the individual (buy and sell) orders follows a power law with similar exponent $\beta \sim \alpha \sim 3/2$. 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 $\gamma \sim 2 \alpha \sim 3$. These results are consistent with recent experimental measurements of these power law exponents ([Maslov 2001] for $\beta$ and [Gopikrishnan et al. 1999] for $\gamma$).

Suggested Citation

  • Sorin Solomon & Peter Richmond, 2001. "Power Laws of Wealth, Market Order Volumes and Market Returns," Papers cond-mat/0102423, arXiv.org, revised Apr 2001.
  • Handle: RePEc:arx:papers:cond-mat/0102423
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    References listed on IDEAS

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    1. Sorin Solomon & Moshe Levy, 1996. "Spontaneous Scaling Emergence In Generic Stochastic Systems," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 7(05), pages 745-751.
    2. Masanao Aoki & Hiroshi Yoshikawa, 1999. "Demand Creation and Economic Growth," CIRJE F-Series CIRJE-F-43, CIRJE, Faculty of Economics, University of Tokyo.
    3. 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.
    4. 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.
    5. Moshe Levy & Sorin Solomon, 1996. "Power Laws Are Logarithmic Boltzmann Laws," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 595-601.
    6. Sergei Maslov & Mark Mills, 2001. "Price fluctuations from the order book perspective - empirical facts and a simple model," Papers cond-mat/0102518, arXiv.org.
    7. Blank, Aharon & Solomon, Sorin, 2000. "Power laws in cities population, financial markets and internet sites (scaling in systems with a variable number of components)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(1), pages 279-288.
    8. Zhi-Feng Huang & Sorin Solomon, 2000. "Power, Levy, Exponential and Gaussian Regimes in Autocatalytic Financial Systems," Papers cond-mat/0008026, arXiv.org.
    9. 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.
    10. Sorin Solomon & Peter Richmond, 2000. "Stability of Pareto-Zipf Law in Non-Stationary Economies," Papers cond-mat/0012479, arXiv.org, revised Jan 2001.
    11. P. Richmond, 2001. "Power law distributions and dynamic behaviour of stock markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(4), pages 523-526, April.
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