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

Listed author(s):
  • 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)

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.

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Article provided by MDPI, Open Access Journal in its journal Risks.

Volume (Year): 2 (2014)
Issue (Month): 4 (October)
Pages: 1-9

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Handle: RePEc:gam:jrisks:v:2:y:2014:i:4:p:425-433:d:41048
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  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.
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