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Generalized Lotka-Volterra (GLV) Models of Stock Markets

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  • Sorin Solomon

    (Rakah lnstitute of Physics, Hebrew University of Jerusalem, Israel)

Abstract

The Generalized Lotka-Volterra (GLV) model:\[ w_i(t + 1) = \lambda w_i(t) + a \bar{w}(t) - c\bar{w}(t)w_i(t)\ \,,\ i = 1,\ldots \ldots, N \]provides a general method to simulate, analyze and understand a wide class of phenomena that are characterized by power-law probability distributions:\[ P(w)dw \sim w^{-1-\alpha}dw (\alpha \ge 1) \]and truncated Levy flights fluctuations$L_\alpha(\bar{w})$. We show how the model applies to economic systems.

Suggested Citation

  • Sorin Solomon, 2000. "Generalized Lotka-Volterra (GLV) Models of Stock Markets," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 3(01n04), pages 301-322.
    • Handle: RePEc:wsi:acsxxx:v:03:y:2000:i:01n04:n:s0219525900000224
    DOI: 10.1142/S0219525900000224
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    Citations

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    Cited by:

    1. Patriarca, Marco & Chakraborti, Anirban & Germano, Guido, 2006. "Influence of saving propensity on the power-law tail of the wealth distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 723-736.
    2. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2007. "Agent-based Models of Financial Markets," Papers physics/0701140, arXiv.org.
    3. Dong, Yang & Wen, Shu-hui & Hu, Xiao-bing & Li, Jiang-Cheng, 2020. "Stochastic resonance of drawdown risk in energy market prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    4. Chakrabarti, Anindya S., 2016. "Stochastic Lotka–Volterra equations: A model of lagged diffusion of technology in an interconnected world," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 214-223.
    5. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
    6. G. Yaari & D. Stauffer & S. Solomon, 2008. "Intermittency and Localization," Papers 0802.3541, arXiv.org, revised Mar 2008.
    7. Chakrabarti, Anindya S., 2015. "Stochastic Lotka-Volterra equations: A model of lagged diffusion of technology in an interconnected world," IIMA Working Papers WP2015-08-05, Indian Institute of Management Ahmedabad, Research and Publication Department.
    8. Scalas, Enrico & Gallegati, Mauro & Guerci, Eric & Mas, David & Tedeschi, Alessandra, 2006. "Growth and allocation of resources in economics: The agent-based approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 86-90.
    9. Zhong, Guang-Yan & He, Feng & Li, Jiang-Cheng & Mei, Dong-Cheng & Tang, Nian-Sheng, 2019. "Coherence resonance-like and efficiency of financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    10. Sorin Solomon & Moshe Levy, 2000. "Market Ecology, Pareto Wealth Distribution and Leptokurtic Returns in Microscopic Simulation of the LLS Stock Market Model," Papers cond-mat/0005416, arXiv.org.

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