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Conditions for bubbles to arise under heterogeneous beliefs

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  • Seunghyun Lee
  • Hyungbin Park

Abstract

This paper studies the equilibrium price of a continuous time asset traded in a market with heterogeneous investors. We consider a positive mean reverting asset and two groups of investors who have different beliefs on the speed of mean reversion and the mean level. We provide an equivalent condition for bubbles to exist and show that price bubbles may not form even though there are heterogeneous beliefs. This condition is directly related to the drift term of the asset. In addition, we characterize the minimal equilibrium price as a unique $C^2$ solution of a differential equation and express it using confluent hypergeometric functions.

Suggested Citation

  • Seunghyun Lee & Hyungbin Park, 2020. "Conditions for bubbles to arise under heterogeneous beliefs," Papers 2012.13753, arXiv.org, revised Oct 2021.
    • Handle: RePEc:arx:papers:2012.13753
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    References listed on IDEAS

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    1. Xi Chen & Robert Kohn, 2011. "Asset price bubbles from heterogeneous beliefs about mean reversion rates," Finance and Stochastics, Springer, vol. 15(2), pages 221-241, June.
    2. Johannes Muhle-Karbe & Marcel Nutz & Xiaowei Tan, 2019. "Asset Pricing with Heterogeneous Beliefs and Illiquidity," Papers 1905.05730, arXiv.org, revised Mar 2020.
    3. Xi Chen & Robert Kohn, 2013. "Erratum to: Asset price bubbles from heterogeneous beliefs about mean reversion rates," Finance and Stochastics, Springer, vol. 17(1), pages 225-226, January.
    4. 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.
    5. Wei Xiong, 2013. "Bubbles, Crises, and Heterogeneous Beliefs," NBER Working Papers 18905, National Bureau of Economic Research, Inc.
    6. Johannes Muhle‐Karbe & Marcel Nutz & Xiaowei Tan, 2020. "Asset pricing with heterogeneous beliefs and illiquidity," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1392-1421, October.
    7. J. Michael Harrison & David M. Kreps, 1978. "Speculative Investor Behavior in a Stock Market with Heterogeneous Expectations," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 92(2), pages 323-336.
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