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Mean Variance Preferences, Expectations Formation, And The Dynamics Of Random Asset Prices

  • Volker Böhm
  • Carl Chiarella

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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Article provided by Wiley Blackwell in its journal Mathematical Finance.

Volume (Year): 15 (2005)
Issue (Month): 1 ()
Pages: 61-97

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Handle: RePEc:bla:mathfi:v:15:y:2005:i:1:p:61-97
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  1. Xue-Zhong He & Carl Chiarella, 1999. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset-Pricing Model," Computing in Economics and Finance 1999 223, Society for Computational Economics.
  2. Volker Böhm & Nicole Deutscher & Jan Wenzelburger, 2000. "Endogenous Random Asset Prices in Overlapping Generations Economies," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 23-38.
  3. repec:att:wimass:9530 is not listed on IDEAS
  4. B hm, Volker & Wenzelburger, Jan, 2002. "Perfect Predictions In Economic Dynamical Systems With Random Perturbations," Macroeconomic Dynamics, Cambridge University Press, vol. 6(05), pages 687-712, November.
  5. repec:att:wimass:9621 is not listed on IDEAS
  6. Chiarella, Carl, 1990. "Excessive exchange rate variability : A possible explanation using nonlinear economic dynamics," European Journal of Political Economy, Elsevier, vol. 6(3), pages 315-352, December.
  7. Brock, W.A. & Hommes, C.H., 1996. "A Rational Route to Randomness," Working papers 9530r, Wisconsin Madison - Social Systems.
  8. 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.
  9. Chiarella, Carl & He, Xue-Zhong, 2003. "Dynamics of beliefs and learning under aL-processes -- the heterogeneous case," Journal of Economic Dynamics and Control, Elsevier, vol. 27(3), pages 503-531, January.
  10. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-84, March.
  11. Stapleton, R C & Subrahmanyam, Marti G, 1978. "A Multiperiod Equilibrium Asset Pricing Model," Econometrica, Econometric Society, vol. 46(5), pages 1077-96, September.
  12. 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.
  13. Balasko, Yves & Royer, Daniel, 1996. "Stability of Competitive Equilibrium with Respect to Recursive and Learning Processes," Journal of Economic Theory, Elsevier, vol. 68(2), pages 319-348, February.
  14. 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.
  15. Schonhofer, Martin, 1999. "Chaotic Learning Equilibria," Journal of Economic Theory, Elsevier, vol. 89(1), pages 1-20, November.
  16. Eichberger, Jurgen & Harper, Ian R., 1997. "Financial Economics," OUP Catalogue, Oxford University Press, number 9780198775409, July.
  17. Bullard James, 1994. "Learning Equilibria," Journal of Economic Theory, Elsevier, vol. 64(2), pages 468-485, December.
  18. 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.
  19. Jan Wenzelburger & Volker Boehm, 2004. "On the performance of efficient portfolios," Computing in Economics and Finance 2004 197, Society for Computational Economics.
  20. B hm, Volker & Wenzelburger, Jan, 1999. "Expectations, Forecasting, And Perfect Foresight," Macroeconomic Dynamics, Cambridge University Press, vol. 3(02), pages 167-186, June.
  21. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
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