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Mean Variance Preferences, Expectations Formation, and the Dynamics of Random Asset Prices

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Abstract

This paper analyzes the dynamics of a general explicit random price process of finitely many assets in an economy with overlapping generations of heterogeneous consumers forming optimal portfolios, extending the one dimensional investigation of Bohm, Deutscher and Wenzelburger (2000). Consumers maximize expected utility with respect to subjective transition probabilities defined by Markov kernels. Given a forecasting rule (predictor) and an exogeneous stochastic process of producer dividends, the dynamics of the economy is described as a random dynamical system in the sense of Arnold (1998). The paper investigates existence and stability of random fixed points (invariant measures) for mean-variance preferences under various forecasting schemes, including unbiased predictions as well as OLS forecasting. Numerical simulations show the stability and the performance of the different predictors for linear mean-variance preferences. Alternative random dividend processes are provided.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp46.pdf
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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 46.

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Date of creation: 01 Oct 2000
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Handle: RePEc:uts:rpaper:46

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Keywords: random dynamical systems; expectations; learning; random asset pricing; mean variance preferences;

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  1. Evans, George W. & Honkapohja, Seppo, 1999. "Learning dynamics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 7, pages 449-542 Elsevier.
  2. Brock, W.A. & Hommes, C.H., 1996. "A Rational Route to Randomness," Working papers 9530r, Wisconsin Madison - Social Systems.
  3. repec:att:wimass:9621 is not listed on IDEAS
  4. 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.
  5. Eichberger, Jurgen & Harper, Ian R., 1997. "Financial Economics," OUP Catalogue, Oxford University Press, number 9780198775409, September.
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