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Heterogeneous Beliefs, Risk and Learning in a Simple Asset-Pricing Model

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Xue-Zhong He () (University of Technology, Sydney)
Carl Chiarella () (University of Technology, Sydney)

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Abstract

Following the concept of "adaptively rational equilibrium", Brock and Hommes establish a simple present discounted value asset-pricing model with heterogeneous beliefs. Agents adapt their beliefs over time by choosing from different predictors or expectations functions, based upon their past performance as measured by realised profits. As the intensity of choice to switch predictors increases, they have observed several bifurcation routes to complicated asset-price fluctuations. In this paper we extend this model to incorporate different risk attitudes of different types of investors and allow for more sophisticated learning schemes. Using both bifurcation theory and numerical analysis, we investigate the effects on the dynamics of the model of different risk aversion coefficients and different learning schemes. We also systematically investigate the effect of external noise on the system. We find that the resulting dynamical behaviour is considerably enriched and has some significant differences compared to the original Brock-Hommes analysis.

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Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 1999 with number 223.

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Date of creation: 01 Mar 1999
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Handle: RePEc:sce:scecf9:223

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Postal: CEF99, Boston College, Department of Economics, Chestnut Hill MA 02467 USA
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  1. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August. [Downloadable!] (restricted)
  2. Summers, Lawrence H, 1986. " Does the Stock Market Rationally Reflect Fundamental Values?," Journal of Finance, American Finance Association, vol. 41(3), pages 591-601, July. [Downloadable!] (restricted)
  3. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, vol. 14(3), pages 299-329, December. [Downloadable!] (restricted)
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  4. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, School of Finance and Economics, University of Technology, Sydney. [Downloadable!]
  5. Sethi, Rajiv, 1996. "Endogenous regime switching in speculative markets," Structural Change and Economic Dynamics, Elsevier, vol. 7(1), pages 99-118, March. [Downloadable!] (restricted)
  6. Reiner Franke & Tim Nesemann, 1999. "Two destabilizing strategies may be jointly stabilizing," Journal of Economics, Springer, vol. 69(1), pages 1-18, February. [Downloadable!] (restricted)
  7. De Long, J Bradford & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1990. "Noise Trader Risk in Financial Markets," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 703-38, August. [Downloadable!] (restricted)
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  8. Franke, Reiner & Sethi, Rajiv, 1998. "Cautious trend-seeking and complex asset price dynamics," Research in Economics, Elsevier, vol. 52(1), pages 61-79, March. [Downloadable!] (restricted)
  9. Campbell, John Y & Kyle, Albert S, 1993. "Smart Money, Noise Trading and Stock Price Behaviour," Review of Economic Studies, Blackwell Publishing, vol. 60(1), pages 1-34, January. [Downloadable!] (restricted)
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  10. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October. [Downloadable!] (restricted)
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  11. repec:att:wimass:19976 is not listed on IDEAS
  12. Lux, Thomas, 1997. "Time variation of second moments from a noise trader/infection model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 1-38, November. [Downloadable!] (restricted)
  13. ., ., 1997. "," Journal of Accounting and Economics, Elsevier, vol. 24(2), pages 127-127, December. [Downloadable!] (restricted)
  14. Iori, Giulia, 2002. "A microsimulation of traders activity in the stock market: the role of heterogeneity, agents' interactions and trade frictions," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 269-285, October. [Downloadable!] (restricted)
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  15. repec:att:wimass:199530r is not listed on IDEAS
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