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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.

Suggested Citation

  • Volker Bohm & Carl Chiarella, 2000. "Mean Variance Preferences, Expectations Formation, and the Dynamics of Random Asset Prices," Research Paper Series 46, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:46
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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.
    2. Stapleton, R C & Subrahmanyam, Marti G, 1978. "A Multiperiod Equilibrium Asset Pricing Model," Econometrica, Econometric Society, vol. 46(5), pages 1077-1096, September.
    3. Xue-Zhong He, 2004. "Dynamics of Beliefs and Learning Under aL-Processes—The Homogeneous Case," International Symposia in Economic Theory and Econometrics, in: Economic Complexity, pages 363-390, Emerald Group Publishing Limited.
    4. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-781, July.
    5. Bullard James, 1994. "Learning Equilibria," Journal of Economic Theory, Elsevier, vol. 64(2), pages 468-485, December.
    6. William A. Brock & Cars H. Hommes, 2001. "A Rational Route to Randomness," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 16, pages 402-438, Edward Elgar Publishing.
    7. Chiarella, Carl, 1988. "The cobweb model: Its instability and the onset of chaos," Economic Modelling, Elsevier, vol. 5(4), pages 377-384, October.
    8. 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.
    9. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    10. Schonhofer, Martin, 1999. "Chaotic Learning Equilibria," Journal of Economic Theory, Elsevier, vol. 89(1), pages 1-20, November.
    11. Bohm, Volker & Wenzelburger, Jan, 2005. "On the performance of efficient portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 721-740, April.
    12. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    13. 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, January.
    14. Blaise Allaz & B. Dumas, 1996. "Financial Securities - Market Equilibrium and Pricing Methods," Post-Print hal-00511816, HAL.
    15. Chiarella, Carl & He, Xue-Zhong, 2002. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model," Computational Economics, Springer;Society for Computational Economics, vol. 19(1), pages 95-132, February.
    16. 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.
    17. Carl Chiarella & Xue-Zhong He, 2000. "Stability of Competitive Equilibria with Heterogeneous Beliefs and Learning," Research Paper Series 37, Quantitative Finance Research Centre, University of Technology, Sydney.
    18. Böhm, Volker & Wenzelburger, Jan, 1999. "Expectations, Forecasting, And Perfect Foresight," Macroeconomic Dynamics, Cambridge University Press, vol. 3(2), pages 167-186, June.
    19. Chiarella, Carl & He, Xue-Zhong, 2003. "Heterogeneous Beliefs, Risk, And Learning In A Simple Asset-Pricing Model With A Market Maker," Macroeconomic Dynamics, Cambridge University Press, vol. 7(4), pages 503-536, September.
    20. 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.
    21. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    22. Böhm, Volker & Wenzelburger, Jan, 2002. "Perfect Predictions In Economic Dynamical Systems With Random Perturbations," Macroeconomic Dynamics, Cambridge University Press, vol. 6(5), pages 687-712, November.
    23. LeRoy,Stephen F. & Werner,Jan, 2014. "Principles of Financial Economics," Cambridge Books, Cambridge University Press, number 9781107024120, February.
    24. Martin Schonhofer, "undated". "Chaotic Learning Equilibria," Computing in Economics and Finance 1997 121, Society for Computational Economics.
    25. 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 363-384, March.
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    More about this item

    Keywords

    random dynamical systems; expectations; learning; random asset pricing; mean variance preferences;
    All these keywords.

    JEL classification:

    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • O16 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Financial Markets; Saving and Capital Investment; Corporate Finance and Governance

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