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

## Author

Listed:
• 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 measurements.

## Suggested Citation

• Zhi-Feng Huang, Sorin Solomon*, 2001. "Power, Levy, Exponential and Gaussian Regimes in Autocatalytic Financial Systems," Computing in Economics and Finance 2001 12, Society for Computational Economics.
• Handle: RePEc:sce:scecf1:12
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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. 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.
3. Mikhail Goykhman, 2017. "Wealth dynamics in a sentiment-driven market," Papers 1705.07092, arXiv.org.
4. 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.
5. 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.
6. 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.
7. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2007. "Agent-based Models of Financial Markets," Papers physics/0701140, arXiv.org.
8. 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.
9. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
10. 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.
11. repec:eee:phsmap:v:488:y:2017:i:c:p:132-148 is not listed on IDEAS

### Keywords

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

### JEL classification:

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

### NEP fields

This paper has been announced in the following NEP Reports:

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