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Power, Lévy, exponential and Gaussian-like regimes in autocatalytic financial systems

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  • Z.F. Huang

    (Institute for Theoretical Physics, Cologne University, 50923 Köln, Germany)

  • S. Solomon

    (Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel)

Abstract

We study by theoretical analysis and by direct numerical simulation the dynamics of a wide class of asynchronous stochastic systems composed of many autocatalytic degrees of freedom. We describe the generic emergence of truncated power laws in the size distribution of their individual elements. The exponents α of these power laws are time independent and depend only on the way the elements with very small values are treated. These truncated power laws determine the collective time evolution of the system. In particular the global stochastic fluctuations of the system differ from the normal Gaussian noise according to the time and size scales at which these fluctuations are considered. We describe the ranges in which these fluctuations are parameterized respectively by: the Lévy regime α 2), and the exponential decay. Finally we relate these results to the large exponent power laws found in the actual behavior of the stock markets and to the exponential cut-off detected in certain recent measurement.

Suggested Citation

  • Z.F. Huang & S. Solomon, 2001. "Power, Lévy, exponential and Gaussian-like regimes in autocatalytic financial systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(4), pages 601-607, April.
    • Handle: RePEc:spr:eurphb:v:20:y:2001:i:4:d:10.1007_pl00011114
    DOI: 10.1007/PL00011114
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    Citations

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    Cited by:

    1. Sorin Solomon & Nataša Golo, 2015. "Microeconomic structure determines macroeconomic dynamics: Aoki defeats the representative agent," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(1), pages 5-30, April.
    2. Mikhail Goykhman, 2017. "Wealth dynamics in a sentiment-driven market," Papers 1705.07092, arXiv.org.
    3. Masanao Aoki & Hiroshi Yoshikawa, 2006. "Stock Prices and the Real Economy: Power Law versus Exponential Distributions," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 1(1), pages 45-73, May.
    4. Goykhman, Mikhail, 2017. "Wealth dynamics in a sentiment-driven market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 488(C), pages 132-148.

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