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Superreplication under Model Uncertainty in Discrete Time


  • Marcel Nutz


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.

Suggested Citation

  • Marcel Nutz, 2013. "Superreplication under Model Uncertainty in Discrete Time," Papers 1301.3227,, revised Feb 2014.
  • Handle: RePEc:arx:papers:1301.3227

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    References listed on IDEAS

    1. Bruno Bouchard & Ludovic Moreau & Marcel Nutz, 2012. "Stochastic target games with controlled loss," Papers 1206.6325,, revised Apr 2014.
    2. Pierre Henry-Labord`ere & Jan Ob{l}'oj & Peter Spoida & Nizar Touzi, 2012. "The maximum maximum of a martingale with given $n$ marginals," Papers 1203.6877,, revised Jan 2016.
    3. Ariel Neufeld & Marcel Nutz, 2012. "Superreplication under Volatility Uncertainty for Measurable Claims," Papers 1208.6486,, revised Apr 2013.
    4. Frank Riedel, 2011. "Finance Without Probabilistic Prior Assumptions," Papers 1107.1078,
    5. 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.
    6. Mathias Beiglbock & Pierre Henry-Labord`ere & Friedrich Penkner, 2011. "Model-independent Bounds for Option Prices: A Mass Transport Approach," Papers 1106.5929,, revised Feb 2013.
    7. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
    8. Marcel Nutz & H. Mete Soner, 2010. "Superhedging and Dynamic Risk Measures under Volatility Uncertainty," Papers 1011.2958,, revised Jun 2012.
    9. Pierre Henry-Labordere & Jan Obloj & Peter Spoida & Nizar Touzi, 2013. "Maximum Maximum of Martingales given Marginals," Working Papers hal-00684005, HAL.
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    Cited by:

    1. Beatrice Acciaio & Martin Larsson, 2016. "Semi-static completeness and robust pricing by informed investors," LSE Research Online Documents on Economics 68502, London School of Economics and Political Science, LSE Library.
    2. Johannes Muhle-Karbe & Marcel Nutz, 2016. "A Risk-Neutral Equilibrium Leading to Uncertain Volatility Pricing," Papers 1612.09152,, revised Jan 2018.
    3. repec:spr:finsto:v:21:y:2017:i:4:d:10.1007_s00780-017-0342-6 is not listed on IDEAS
    4. Mathias Beiglbock & Marcel Nutz & Nizar Touzi, 2015. "Complete Duality for Martingale Optimal Transport on the Line," Papers 1507.00671,, revised Jun 2016.
    5. Sebastian Herrmann & Johannes Muhle-Karbe, 2017. "Model Uncertainty, Recalibration, and the Emergence of Delta-Vega Hedging," Papers 1704.04524,
    6. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008,, revised Mar 2015.
    7. Christopher W. Miller, 2016. "A Duality Result for Robust Optimization with Expectation Constraints," Papers 1610.01227,
    8. Marco Maggis & Thilo Meyer-Brandis & Gregor Svindland, 2016. "The Fatou Closedness under Model Uncertainty," Papers 1610.04085,, revised Jul 2017.
    9. Bruno Bouchard & Marcel Nutz, 2016. "Consistent price systems under model uncertainty," Finance and Stochastics, Springer, vol. 20(1), pages 83-98, January.
    10. Sebastian Herrmann & Johannes Muhle-Karbe & Frank Thomas Seifried, 2017. "Hedging with small uncertainty aversion," Finance and Stochastics, Springer, vol. 21(1), pages 1-64, January.
    11. Beatrice Acciaio & Martin Larsson, 2015. "Semi-static completeness and robust pricing by informed investors," Papers 1510.01890,, revised Sep 2016.
    12. Bruno Bouchard & Marcel Nutz, 2016. "Consistent price systems under model uncertainty," Finance and Stochastics, Springer, vol. 20(1), pages 83-98, January.
    13. Sebastian E. Ferrando & Alfredo L. Gonzalez & Ivan L. Degano & Massoome Rahsepar, 2014. "Discrete, Non Probabilistic Market Models. Arbitrage and Pricing Intervals," Papers 1407.1769,, revised Nov 2015.
    14. Marcel Nutz & Florian Stebegg, 2016. "Canonical Supermartingale Couplings," Papers 1609.02867,, revised Nov 2017.
    15. repec:spr:finsto:v:22:y:2018:i:2:d:10.1007_s00780-018-0356-8 is not listed on IDEAS

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