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A dynamic stochastic model of asset pricing with heterogeneous beliefs

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Author Info

  • Serena Brianzoni

    (University of Macerata)

  • Roy Cerqueti,

    (University of Macerata)

  • Elisabetta Michetti

    (University of Macerata)

Abstract

This paper presents a new stochastic model of asset pricing, based on agents with heterogeneous beliefs. Forecasting rules of all agents are characterized by a stochastic term that works as an agent-based time dependent weight of the conditional expectation of the fundamental. Since we consider the presence of an imitative behavior between agents, these weights depend stochastically on the type-distribution of agents. The resulting dynamical system is firstly analyzed in a deterministic framework. Starting from the results obtained in the deterministic case, the model is lastly explored by reintroducing randomness. The deterministic study aims at providing the existence of a region in the parameters plane where the unique possible dynamics is the convergence to a steady state, while complexity is exhibited outside such region. This region is also analyzed by reintroducing stochasticity and we provide an explicit formula for its probability measure. Our findings are in agreement with the economic meaning of the parameters. Finally, we propose a bayesian analysis, in order to explore the distribution of the adjustment term of the proportion of agents.

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Bibliographic Info

Paper provided by Macerata University, Department of Finance and Economic Sciences in its series Working Papers with number 46-2008.

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Date of creation: Oct 2008
Date of revision: Oct 2008
Handle: RePEc:mcr:wpdief:wpaper00046

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Keywords: Stochastic asset pricing; probability measure; heterogeneous beliefs; imitative behaviour; complex dynamics; Developing Countries;

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References

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  1. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
  2. V. V. Chari & Patrick J. Kehoe, 2000. "Financial crises as herds," Working Papers 600, Federal Reserve Bank of Minneapolis.
  3. Cars H. Hommes, 2005. "Heterogeneous Agent Models in Economics and Finance," Tinbergen Institute Discussion Papers 05-056/1, Tinbergen Institute.
  4. repec:att:wimass:9506 is not listed on IDEAS
  5. Hommes, Cars H., 1994. "Dynamics of the cobweb model with adaptive expectations and nonlinear supply and demand," Journal of Economic Behavior & Organization, Elsevier, vol. 24(3), pages 315-335, August.
  6. Avery, Christopher & Zemsky, Peter, 1998. "Multidimensional Uncertainty and Herd Behavior in Financial Markets," American Economic Review, American Economic Association, vol. 88(4), pages 724-48, September.
  7. repec:att:wimass:9621 is not listed on IDEAS
  8. Cars H. Hommes, 2001. "Financial Markets as Nonlinear Adaptive Evolutionary Systems," Tinbergen Institute Discussion Papers 01-014/1, Tinbergen Institute.
  9. Chamley, Christophe & Gale, Douglas, 1994. "Information Revelation and Strategic Delay in a Model of Investment," Econometrica, Econometric Society, vol. 62(5), pages 1065-85, September.
  10. Bikhchandani, Sushil & Hirshleifer, David & Welch, Ivo, 1992. "A Theory of Fads, Fashion, Custom, and Cultural Change in Informational Cascades," Journal of Political Economy, University of Chicago Press, vol. 100(5), pages 992-1026, October.
  11. Kim, Jae-Young, 2000. "Detection of change in persistence of a linear time series," Journal of Econometrics, Elsevier, vol. 95(1), pages 97-116, March.
  12. Busetti, Fabio & Taylor, A. M. Robert, 2004. "Tests of stationarity against a change in persistence," Journal of Econometrics, Elsevier, vol. 123(1), pages 33-66, November.
  13. John Conlisk, 1996. "Why Bounded Rationality?," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 669-700, June.
  14. 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.
  15. Junsoo Lee & Mark C. Strazicich, 2004. "Minimum LM Unit Root Test with One Structural Break," Working Papers 04-17, Department of Economics, Appalachian State University.
  16. Amsler, Christine & Lee, Junsoo, 1995. "An LM Test for a Unit Root in the Presence of a Structural Change," Econometric Theory, Cambridge University Press, vol. 11(02), pages 359-368, February.
  17. William A. Brock & Cars H. Hommes, 1995. "Rational Routes to Randomness," Working Papers 95-03-029, Santa Fe Institute.
  18. Alan Kirman, 2006. "Heterogeneity in Economics," Journal of Economic Interaction and Coordination, Springer, vol. 1(1), pages 89-117, May.
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Cited by:
  1. Pietro Dindo & Jan Tuinstra, 2010. "A class of evolutionary models for participation games with negative feedback," LEM Papers Series 2010/14, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.

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