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Shifting martingale measures and the birth of a bubble as a submartingale

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  • Francesca Biagini
  • Hans Föllmer
  • Sorin Nedelcu

Abstract

In an incomplete financial market model, we study a flow in the space of equivalent martingale measures and the corresponding shifting perception of the fundamental value of a given asset. This allows us to capture the birth of a perceived bubble and to describe it as an initial submartingale which then turns into a supermartingale before it falls back to its initial value zero. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Francesca Biagini & Hans Föllmer & Sorin Nedelcu, 2014. "Shifting martingale measures and the birth of a bubble as a submartingale," Finance and Stochastics, Springer, vol. 18(2), pages 297-326, April.
    • Handle: RePEc:spr:finsto:v:18:y:2014:i:2:p:297-326
    DOI: 10.1007/s00780-013-0221-8
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Robert A. Jarrow, 2015. "Asset Price Bubbles," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 201-218, December.
    2. Philip Stahl & Jérôme Blauth, 2024. "Martingale defects in the volatility surface and bubble conditions in the underlying," Review of Derivatives Research, Springer, vol. 27(1), pages 85-111, April.
    3. Philip Protter & Aditi Dandapani, 2019. "Strict Local Martingales and the Khasminskii test for Explosions," Papers 1903.02383, arXiv.org.
    4. David Criens & Kathrin Glau & Zorana Grbac, 2015. "Martingale property of exponential semimartingales: a note on explicit conditions and applications to financial models," Papers 1506.08127, arXiv.org, revised Aug 2016.
    5. Dandapani, Aditi & Protter, Philip, 2022. "Strict local martingales and the Khasminskii test for explosions," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 716-728.
    6. Martin HERDEGEN & Martin SCHWEIZER, 2015. "Economics-Based Financial Bubbles (and Why They Imply Strict Local Martingales)," Swiss Finance Institute Research Paper Series 15-05, Swiss Finance Institute.
    7. Beissner, Patrick & Rosazza Gianin, Emanuela, 2018. "The Term Structure of Sharpe Ratios and Arbitrage-Free Asset Pricing in Continuous Time," Rationality and Competition Discussion Paper Series 72, CRC TRR 190 Rationality and Competition.
    8. Johannes Muhle-Karbe & Marcel Nutz, 2018. "A risk-neutral equilibrium leading to uncertain volatility pricing," Finance and Stochastics, Springer, vol. 22(2), pages 281-295, April.
    9. Christoph Belak & Sören Christensen & Olaf Menkens, 2016. "Worst-Case Portfolio Optimization In A Market With Bubbles," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-36, March.
    10. Martin Herdegen & Dorte Kreher, 2021. "Bubbles in discrete time models," Papers 2104.12740, arXiv.org, revised Jul 2022.
    11. Francesca Biagini & Thomas Reitsam, 2019. "Asset Price Bubbles in market models with proportional transaction costs," Papers 1911.10149, arXiv.org, revised Dec 2020.
    12. Martin Herdegen & Martin Schweizer, 2016. "Strong Bubbles And Strict Local Martingales," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-44, June.
    13. Martin Herdegen & Dörte Kreher, 2022. "Bubbles in discrete-time models," Finance and Stochastics, Springer, vol. 26(4), pages 899-925, October.
    14. Aditi Dandapani & Philip Protter, 2019. "Strict Local Martingales Via Filtration Enlargement," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(01), pages 1-28, December.
    15. David Criens & Kathrin Glau & Zorana Grbac, 2017. "Martingale property of exponential semimartingales: a note on explicit conditions and applications to asset price and Libor models," Post-Print hal-03898993, HAL.
    16. Roseline Bilina Falafala & Robert A. Jarrow & Philip Protter, 2016. "Relative asset price bubbles," Annals of Finance, Springer, vol. 12(2), pages 135-160, May.

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    More about this item

    Keywords

    Bubbles; Strict local martingales; Submartingales; Equivalent martingale measures; Stochastic volatility; 91G99; 60G07; 60G44; C60; C65; G12;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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