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A dynamical stochastic coupled model for financial markets

Author

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  • Govindan, T.E.
  • Ibarra-Valdez, Carlos
  • Ruiz de Chávez, J.

Abstract

A model coupling a deterministic dynamical system which represents trading, with a stochastic one that represents asset prices evolution is presented. Both parts of the model have connections with well established dynamic models in mathematical economics and finance. The main objective is to represent the double feedback between trading dynamics (the demand/supply interaction) and price dynamics (assumed as largely random). We present the model, and address to some extent existence and uniqueness, continuity with respect to initial conditions and stability of solutions. The non-Lipschitz case is briefly considered as well.

Suggested Citation

  • Govindan, T.E. & Ibarra-Valdez, Carlos & Ruiz de Chávez, J., 2007. "A dynamical stochastic coupled model for financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 317-328.
    • Handle: RePEc:eee:phsmap:v:381:y:2007:i:c:p:317-328
    DOI: 10.1016/j.physa.2007.03.014
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    References listed on IDEAS

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    1. Thomas Lux & Michele Marchesi, 2000. "Volatility Clustering In Financial Markets: A Microsimulation Of Interacting Agents," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 675-702.
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    3. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
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    1. Basak, Gopal K. & Das, Pranab Kumar & Rohit, Allena, 2019. "Coupled dynamics with an external system and application to international finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 409-432.

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