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

## Author Info

• 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

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## Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2001 with number 12.

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Handle: RePEc:sce:scecf1:12

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Web page: http://www.econometricsociety.org/conference/SCE2001/SCE2001.html

## Related research

Keywords: stochastic model; returns distribution; gaussian; levy distribution; power tails;

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

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## Citations

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Cited by:
1. Masanao Aoki & Hiroshi Yoshikawa, 2006. "Stock Prices and the Real Economy: Power Law versus Exponential Distributions," Journal of Economic Interaction and Coordination, Springer, vol. 1(1), pages 45-73, May.
2. Marco Raberto & Silvano Cincotti & Sergio Focardi & Michele Marchesi, 2003. "Traders' Long-Run Wealth in an Artificial Financial Market," Computational Economics, Society for Computational Economics, vol. 22(2), pages 255-272, October.
3. 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.

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