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Modeling stock market dynamics based on conservation principles

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  • Alvarez-Ramirez, Jose
  • Ibarra-Valdez, Carlos

Abstract

In this paper, a deterministic framework for modeling stock market dynamics is presented. The model is based on assets conservation principles and consists of a series of differential equations describing the dynamics of assets trading, and a (nonlinear) functional equation describing trade conservation (i.e., what is bought (sold) by one trader is sold (bought) by other traders). In this way, the dynamics of the assets and its price are determined by the trading dynamics. An equilibrium price is achieved when certain demand/supply equations are satisfied. Attention is devoted to a specific case, in which the trading activity is based on trader groups and an infinitely divisible asset. Numerical simulations show that even a single stock market asset with two classes of investors can display oscillatory price dynamics and instability. Moreover, the underlying oscillatory time-series display a discontinuous erratic-type behavior.

Suggested Citation

  • Alvarez-Ramirez, Jose & Ibarra-Valdez, Carlos, 2001. "Modeling stock market dynamics based on conservation principles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 493-511.
    • Handle: RePEc:eee:phsmap:v:301:y:2001:i:1:p:493-511
    DOI: 10.1016/S0378-4371(01)00410-1
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    References listed on IDEAS

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    1. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, vol. 14(3), pages 299-329, December.
    2. De Long, J Bradford, et al, 1990. "Positive Feedback Investment Strategies and Destabilizing Rational Speculation," Journal of Finance, American Finance Association, vol. 45(2), pages 379-395, June.
    3. Bonanno, Giovanni & Lillo, Fabrizio & Mantegna, Rosario N, 2000. "Dynamics of the number of trades of financial securities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(1), pages 136-141.
    4. Alan Kirman, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(1), pages 137-156.
    5. De Bondt, Werner F M & Thaler, Richard, 1985. "Does the Stock Market Overreact?," Journal of Finance, American Finance Association, vol. 40(3), pages 793-805, July.
    6. Kandel, Eugene & Pearson, Neil D, 1995. "Differential Interpretation of Public Signals and Trade in Speculative Markets," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 831-872, August.
    7. Ausloos, M., 2000. "Gas-kinetic theory and Boltzmann equation of share price within an equilibrium market hypothesis and ad hoc strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 385-392.
    8. A. G. Malliaris & Jerome L. Stein, 2005. "Methodological issues in asset pricing: Random walk or chaotic dynamics," World Scientific Book Chapters, in: Economic Uncertainty, Instabilities And Asset Bubbles Selected Essays, chapter 8, pages 85-115, World Scientific Publishing Co. Pte. Ltd..
    9. Jerome L. Stein, 1994. "Can the central bank achieve price stability?," Review, Federal Reserve Bank of St. Louis, issue Mar, pages 175-203.
    10. Takayasu, H. & Takayasu, M., 1999. "Critical fluctuations of demand and supply," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 24-29.
    11. Black, Fischer, 1986. "Noise," Journal of Finance, American Finance Association, vol. 41(3), pages 529-543, July.
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    2. Chen, Wei-Ching, 2008. "Dynamics and control of a financial system with time-delayed feedbacks," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1198-1207.

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