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A Note on the Fundamental Theorem of Asset Pricing under Model Uncertainty

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  • Erhan Bayraktar

    () (Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, USA)

  • Yuchong Zhang

    () (Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, USA)

  • Zhou Zhou

    () (Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, USA)

Abstract

We show that the recent results on the Fundamental Theorem of Asset Pricing and the super-hedging theorem in the context of model uncertainty can be extended to the case in which the options available for static hedging (hedging options) are quoted with bid-ask spreads. In this set-up, we need to work with the notion of robust no-arbitrage which turns out to be equivalent to no-arbitrage under the additional assumption that hedging options with non-zero spread are non-redundant. A key result is the closedness of the set of attainable claims, which requires a new proof in our setting.

Suggested Citation

  • Erhan Bayraktar & Yuchong Zhang & Zhou Zhou, 2014. "A Note on the Fundamental Theorem of Asset Pricing under Model Uncertainty," Risks, MDPI, Open Access Journal, vol. 2(4), pages 1-9, October.
  • Handle: RePEc:gam:jrisks:v:2:y:2014:i:4:p:425-433:d:41048
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    References listed on IDEAS

    as
    1. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    2. Yan Dolinsky & H. Soner, 2014. "Robust hedging with proportional transaction costs," Finance and Stochastics, Springer, vol. 18(2), pages 327-347, April.
    3. Cousot, Laurent, 2007. "Conditions on option prices for absence of arbitrage and exact calibration," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3377-3397, November.
    4. Erhan Bayraktar & Yuchong Zhang, 2016. "Fundamental Theorem of Asset Pricing Under Transaction Costs and Model Uncertainty," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 1039-1054, August.
    5. Mark H. A. Davis & David G. Hobson, 2007. "The Range Of Traded Option Prices," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 1-14.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Arash Fahim & Yu-Jui Huang, 2016. "Model-independent superhedging under portfolio constraints," Finance and Stochastics, Springer, vol. 20(1), pages 51-81, January.
    2. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2014. "Robust Fundamental Theorem for Continuous Processes," Papers 1410.4962, arXiv.org, revised Jul 2015.
    3. Erhan Bayraktar & Zhou Zhou, 2016. "No-arbitrage and hedging with liquid American options," Papers 1605.01327, arXiv.org, revised Jan 2018.
    4. Arash Fahim & Yu-Jui Huang, 2016. "Model-independent superhedging under portfolio constraints," Finance and Stochastics, Springer, vol. 20(1), pages 51-81, January.

    More about this item

    Keywords

    Model uncertainty; bid-ask prices for options; semi-static hedging; non-dominated collection of probability measures; Fundamental Theorem of Asset Pricing; super-hedging; robust no-arbitrage; non-redundant options;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • G0 - Financial Economics - - General
    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services
    • G3 - Financial Economics - - Corporate Finance and Governance
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics
    • M4 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting
    • K2 - Law and Economics - - Regulation and Business Law

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