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Asset Price Bubbles in Complete Markets

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Advances in Mathematical Finance

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Summary

This paper reviews and extends the mathematical finance literature on bubbles in complete markets. We provide a new characterization theorem for bubbles under the standard no-arbitrage framework, showing that bubbles can be of three types. Type 1 bubbles are uniformly integrable martingales, and these can exist with an infinite lifetime. Type 2 bubbles are nonuniformly integrable martingales, and these can exist for a finite, but unbounded, lifetime. Last, Type 3 bubbles are strict local martingales, and these can exist for a finite lifetime only. When one adds a no-dominance assumption (from Merton [24]), only Type 1 bubbles remain. In addition, under Merton’s no-dominance hypothesis, put–call parity holds and there are no bubbles in standard call and put options. Our analysis implies that if one believes asset price bubbles exist and are an important economic phenomena, then asset markets must be incomplete.

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Author information

Authors and Affiliations

  1. Johnson Graduate School of Management, Cornell University, Ithaca, NY 14850, USA

    Robert A. Jarrow

  2. School of Operations Research and Industrial Engineering, College of Engineering Cornell University, Ithaca, NY, 14850, USA

    Philip Protter & Kazuhiro Shimbo

Authors
  1. Robert A. Jarrow
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  2. Philip Protter
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  3. Kazuhiro Shimbo
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Editor information

Editors and Affiliations

  1. Robert H. Smith School of Business Van Munching Hall, University of Maryland, College Park, MD 20742, USA

    Michael C. Fu

  2. Johnson Graduate School of Management 451 Sage Hall, Cornell University, Ithaca, NY 14853, USA

    Robert A. Jarrow

  3. Department of Mathematics, 1326 Stevenson Center Vanderbilt University, Nashville, TN 37240, USA

    Ju-Yi J. Yen

  4. Haskayne School of Business Scurfield Hall, University of Calgary, Calgary, AB T2N 1N4, Canada

    Robert J. Elliott

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© 2007 Birkhäuser Boston

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Jarrow, R.A., Protter, P., Shimbo, K. (2007). Asset Price Bubbles in Complete Markets. In: Fu, M.C., Jarrow, R.A., Yen, JY.J., Elliott, R.J. (eds) Advances in Mathematical Finance. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4545-8_7

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