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Power, Levy, Exponential and Gaussian Regimes in Autocatalytic Financial Systems

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  • Zhi-Feng Huang
  • Sorin Solomon

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 $\alpha$ 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 Levy regime $\alpha 2$), 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

  • Zhi-Feng Huang & Sorin Solomon, 2000. "Power, Levy, Exponential and Gaussian Regimes in Autocatalytic Financial Systems," Papers cond-mat/0008026, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0008026
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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. Aoki, Masanao, 2008. "Thermodynamic limits of macroeconomic or financial models: One- and two-parameter Poisson-Dirichlet models," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 66-84, January.
    3. Solomon, Sorin & Richmond, Peter, 2001. "Power laws of wealth, market order volumes and market returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 188-197.
    4. 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.
    5. Marco Raberto & Silvano Cincotti & Sergio Focardi & Michele Marchesi, 2003. "Traders' Long-Run Wealth in an Artificial Financial Market," Computational Economics, Springer;Society for Computational Economics, vol. 22(2), pages 255-272, October.
    6. Mikhail Goykhman, 2017. "Wealth dynamics in a sentiment-driven market," Papers 1705.07092, arXiv.org.
    7. 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.
    8. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
    9. Masanao Aoki, 2006. "Long-run Behavior of Macroeconomic Models with Heterogeneous Agents: Asymptotic Behavior of One- and Two-Parameter Poisson-Dirichlet Distributions," CIRJE F-Series CIRJE-F-425, CIRJE, Faculty of Economics, University of Tokyo.
    10. Goykhman, Mikhail, 2017. "Wealth dynamics in a sentiment-driven market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 488(C), pages 132-148.
    11. Masanao Aoki, 2006. "Thermodynamic Limits of Macroeconomic or Financial Models: One-and Two-Parameter Poisson-Dirichlet Models (Forthcoming in "Journal of Economic Dynamics and Control", 2007. )," CARF F-Series CARF-F-083, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    12. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2007. "Agent-based Models of Financial Markets," Papers physics/0701140, arXiv.org.

    More about this item

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • G - Financial Economics
    • Z - Other Special Topics

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