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Asset price bubbles from heterogeneous beliefs about mean reversion rates

  • Xi Chen


  • Robert Kohn


Registered author(s):

    Harrison and Kreps showed in 1978 how the heterogeneity of investor beliefs can drive speculation, leading the price of an asset to exceed its intrinsic value. By focusing on an extremely simple market model—a finite-state Markov chain—the analysis of Harrison and Kreps achieved great clarity but limited realism. Here we achieve similar clarity with greater realism, by considering an asset whose dividend rate is a mean-reverting stochastic process. Our investors agree on the volatility, but have different beliefs about the mean reversion rate. We determine the minimum equilibrium price explicitly; in addition, we characterize it as the unique classical solution of a certain linear differential equation. Our example shows, in a simple and transparent manner, how heterogeneous beliefs about the mean reversion rate can lead to everlasting speculation and a permanent “price bubble.” Copyright Springer-Verlag 2011

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    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 15 (2011)
    Issue (Month): 2 (June)
    Pages: 221-241

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    Handle: RePEc:spr:finsto:v:15:y:2011:i:2:p:221-241
    DOI: 10.1007/s00780-010-0124-x
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    1. Jose A. Scheinkman & Wei Xiong, 2003. "Overconfidence and Speculative Bubbles," Journal of Political Economy, University of Chicago Press, vol. 111(6), pages 1183-1219, December.
    2. Dumas, Bernard J & Kurshev, Alexander & Uppal, Raman, 2007. "Equilibrium Portfolio Strategies in the Presence of Sentiment Risk and Excess Volatility," CEPR Discussion Papers 6455, C.E.P.R. Discussion Papers.
    3. J. Bradford De Long & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann,, . "The Survival of Noise Traders in Financial Markets," J. Bradford De Long's Working Papers _123, University of California at Berkeley, Economics Department.
    4. Leonid Kogan & Stephen Ross, 2004. "The Price Impact and Survival of Irrational Traders," 2004 Meeting Papers 35, Society for Economic Dynamics.
    5. J. Michael Harrison & David M. Kreps, 1978. "Speculative Investor Behavior in a Stock Market with Heterogeneous Expectations," The Quarterly Journal of Economics, Oxford University Press, vol. 92(2), pages 323-336.
    6. Hongjun Yan, 2008. "Natural Selection in Financial Markets: Does It Work?," Management Science, INFORMS, vol. 54(11), pages 1935-1950, November.
    7. Radner, Roy, 1972. "Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets," Econometrica, Econometric Society, vol. 40(2), pages 289-303, March.
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