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Dynamical Explanation For The Emergence Of Power Law In A Stock Market Model

Author

Listed:
  • MOSHE LEVY

    (Department of Theoretical Physics, Racah Institute of Physics, Israel)

  • SORIN SOLOMON

    (Department of Theoretical Physics, Racah Institute of Physics, Israel)

  • GIVAT RAM

    (The Hebrew University of Jerusalem, Jerusalem 91904, Israel)

Abstract

Power laws are found in a wide range of different systems: From sand piles to word occurrence frequencies and to the size distribution of cities. The natural emergence of these power laws in so many different systems, which has been called self-organized criticality, seems rather mysterious and awaits a rigorous explanation. In this letter we study the stationary regime of a previously introduced dynamical microscopic model of the stock market. We find that the wealth distribution among investors spontaneously converges to a power law. We are able to explain this phenomenon by simple general considerations. We suggest that similar considerations may explain self-organized criticality in many other systems. They also explain the Levy distribution.

Suggested Citation

  • Moshe Levy & Sorin Solomon & Givat Ram, 1996. "Dynamical Explanation For The Emergence Of Power Law In A Stock Market Model," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 65-72.
    • Handle: RePEc:wsi:ijmpcx:v:07:y:1996:i:01:n:s0129183196000077
    DOI: 10.1142/S0129183196000077
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    Citations

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    Cited by:

    1. Johann Lussange & Ivan Lazarevich & Sacha Bourgeois-Gironde & Stefano Palminteri & Boris Gutkin, 2021. "Modelling Stock Markets by Multi-agent Reinforcement Learning," Computational Economics, Springer;Society for Computational Economics, vol. 57(1), pages 113-147, January.
    2. Predrag R. Jelenković & Jian Tan, 2010. "Modulated Branching Processes, Origins of Power Laws, and Queueing Duality," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 807-829, November.
    3. Johann Lussange & Stefano Vrizzi & Stefano Palminteri & Boris Gutkin, 2024. "Modelling crypto markets by multi-agent reinforcement learning," Papers 2402.10803, arXiv.org.
    4. Jovanovic, Franck & Mantegna, Rosario N. & Schinckus, Christophe, 2019. "When financial economics influences physics: The role of Econophysics," International Review of Financial Analysis, Elsevier, vol. 65(C).
    5. Y. Malevergne & V. F. Pisarenko & D. Sornette, 2003. "Empirical Distributions of Log-Returns: between the Stretched Exponential and the Power Law?," Papers physics/0305089, arXiv.org.

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