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Asset Price and Wealth Dynamics under Heterogeneous Expectations

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  • Xue-Zhong (Tony) He

    (University of Technology Sydney)

  • Carl Chiarella

    (University of Technology Sydney)

Abstract

In order to characterise price and wealth dynamics under the interaction of heterogeneous agents with a CRRA utility, a discrete time stationary wealth dynamics model in terms of return and wealth proportions (among different types of agents) is established. Fundamentalists and chartists are the main heterogeneous agents in the model. It is found that the presence of heterogeneous agents can lead the stationary model to have multiple equilibria. The equilibrium is unstable when the chartist extrapolation rate is high and (locally) stable when the rate is low. The convergence to the equilibrium follows an optimal selection principle --- the return and wealth proportion tends to one of the equilibria, which has relative higher return. The model that is finally developed displays the essential characteristics of the standard asset price dynamics model assumed in continuous time finance in that the asset price is fluctuating around an geometrically growing trend.

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Bibliographic Info

Paper provided by Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance in its series CeNDEF Workshop Papers, January 2001 with number 5A.2.

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Date of creation: 04 Jan 2001
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Handle: RePEc:ams:cdws01:5a.2

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Postal: Dept. of Economics and Econometrics, Universiteit van Amsterdam, Roetersstraat 11, NL - 1018 WB Amsterdam, The Netherlands
Phone: + 31 20 525 52 58
Fax: + 31 20 525 52 83
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Web page: http://www.fee.uva.nl/cendef/
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  1. Carl Chiarella & Xue-Zhong He, 2001. "Dynamics of Beliefs and Learning Under aL Processes - The Homogeneous Case," Research Paper Series 53, Quantitative Finance Research Centre, University of Technology, Sydney.
  2. Carl Chiarella & Xue-Zhong He, 2000. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model with a Market Maker," Research Paper Series 35, Quantitative Finance Research Centre, University of Technology, Sydney.
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  6. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
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  8. Frankel, Jeffrey A & Froot, Kenneth A, 1986. "Understanding the U.S. Dollar in the Eighties: The Expectations of Chartists and Fundamentalists," The Economic Record, The Economic Society of Australia, vol. 0(0), pages 24-38, Supplemen.
  9. Lux, T. & M. Marchesi, . "Scaling and Criticality in a Stochastic Multi-Agent Model of a Financial Market," Discussion Paper Serie B 438, University of Bonn, Germany, revised Jul 1998.
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  13. Lux, Thomas, 1998. "The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(2), pages 143-165, January.
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  26. Gaunersdorfer, A. & Hommes, C.H., 2000. "A Nonlinear Structural Model for Volatility Clustering," CeNDEF Working Papers 00-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
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