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Superreplication under Model Uncertainty in Discrete Time

  • Marcel Nutz
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    We study the superreplication of contingent claims under model uncertainty in discrete time. We show that optimal superreplicating strategies exist in a general measure-theoretic setting; moreover, we characterize the minimal superreplication price as the supremum over all continuous linear pricing functionals on a suitable Banach space. The main ingredient is a closedness result for the set of claims which can be superreplicated from zero capital; its proof relies on medial limits.

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    File URL: http://arxiv.org/pdf/1301.3227
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    Paper provided by arXiv.org in its series Papers with number 1301.3227.

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    Date of creation: Jan 2013
    Date of revision: Feb 2014
    Handle: RePEc:arx:papers:1301.3227
    Contact details of provider: Web page: http://arxiv.org/

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    1. J. Jacod & A.N. Shiryaev, 1998. "Local martingales and the fundamental asset pricing theorems in the discrete-time case," Finance and Stochastics, Springer, vol. 2(3), pages 259-273.
    2. Marcel Nutz & H. Mete Soner, 2010. "Superhedging and Dynamic Risk Measures under Volatility Uncertainty," Papers 1011.2958, arXiv.org, revised Jun 2012.
    3. Bruno Bouchard & Ludovic Moreau & Marcel Nutz, 2012. "Stochastic target games with controlled loss," Papers 1206.6325, arXiv.org, revised Apr 2014.
    4. Mathias Beiglb\"ock & Pierre Henry-Labord\`ere & Friedrich Penkner, 2011. "Model-independent Bounds for Option Prices: A Mass Transport Approach," Papers 1106.5929, arXiv.org, revised Feb 2013.
    5. Pierre Henry-Labordere & Jan Obloj & Peter Spoida & Nizar Touzi, 2012. "The maximum maximum of a martingale with given n marginals," Papers 1203.6877, arXiv.org, revised Sep 2014.
    6. Ariel Neufeld & Marcel Nutz, 2012. "Superreplication under Volatility Uncertainty for Measurable Claims," Papers 1208.6486, arXiv.org, revised Apr 2013.
    7. Pierre Henry-Labordere & Jan Obloj & Peter Spoida & Nizar Touzi, 2013. "Maximum Maximum of Martingales given Marginals," Working Papers hal-00684005, HAL.
    8. Frank Riedel, 2011. "Finance without Probabilistic Prior Assumptions," Working Papers 450, Bielefeld University, Center for Mathematical Economics.
    9. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
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