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A Stochastic Version of Zeeman's Market Model

Author

Listed:
  • Rheinlaender Thorsten

    () (London School of Economics)

  • Steinkamp Marcus

    () (Humboldt University Berlin)

Abstract

In a heterogenous agents framework, we study a randomized version of Zeeman's market model with fundamental and momentum traders. Using methods from random dynamical systems theory, we examine convergence properties of invariant measures which correspond to market equilibria. It turns out that due to a stochastic stabilisation effect the market stays stable up to some critical value of speculative activity. If this threshold is surpassed, sudden trend reversals are possible without being induced by some exogenous shock.

Suggested Citation

  • Rheinlaender Thorsten & Steinkamp Marcus, 2004. "A Stochastic Version of Zeeman's Market Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(4), pages 1-25, December.
    • Handle: RePEc:bpj:sndecm:v:8:y:2004:i:4:n:4
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    References listed on IDEAS

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    1. Hans Föllmer & Martin Schweizer, 1993. "A Microeconomic Approach to Diffusion Models For Stock Prices," Mathematical Finance, Wiley Blackwell, vol. 3(1), pages 1-23.
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    Cited by:

    1. Chiarella, Carl & He, Xue-Zhong & Wang, Duo & Zheng, Min, 2008. "The stochastic bifurcation behaviour of speculative financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3837-3846.
    2. Thomas Lux, 2013. "Inference for systems of stochastic differential equations from discretely sampled data: a numerical maximum likelihood approach," Annals of Finance, Springer, vol. 9(2), pages 217-248, May.
    3. Hommes, C.H., 2005. "Heterogeneous Agent Models in Economics and Finance, In: Handbook of Computational Economics II: Agent-Based Computational Economics, edited by Leigh Tesfatsion and Ken Judd , Elsevier, Amsterdam 2006," CeNDEF Working Papers 05-03, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    4. Chiarella, Carl & He, Xue-Zhong & Zheng, Min, 2011. "An analysis of the effect of noise in a heterogeneous agent financial market model," Journal of Economic Dynamics and Control, Elsevier, vol. 35(1), pages 148-162, January.
    5. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics,in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186 Elsevier.
    6. Rosser Jr., J. Barkley, 2007. "The rise and fall of catastrophe theory applications in economics: Was the baby thrown out with the bathwater?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3255-3280, October.

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