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Model-independent superhedging under portfolio constraints

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  • Arash Fahim
  • Yu-Jui Huang

Abstract

In a discrete-time market, we study model-independent superhedging where the semi-static superhedging portfolio consists of three parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet possibly less liquid, exotic options, and a dynamic trading strategy in risky assets under certain constraints. By considering the limit order book of each tradable exotic option and employing the Monge–Kantorovich theory of optimal transport we establish a general superhedging duality, which admits a natural connection to convex risk measures. With the aid of this duality, we derive a model-independent version of the fundamental theorem of asset pricing. The notion “finite optimal arbitrage profit”, weaker than no-arbitrage, is also introduced. It is worth noting that our method covers a large class of delta and gamma constraints. Copyright Springer-Verlag Berlin Heidelberg 2016

Suggested Citation

  • Arash Fahim & Yu-Jui Huang, 2016. "Model-independent superhedging under portfolio constraints," Finance and Stochastics, Springer, vol. 20(1), pages 51-81, January.
    • Handle: RePEc:spr:finsto:v:20:y:2016:i:1:p:51-81
    DOI: 10.1007/s00780-015-0284-9
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Mathias Beiglbock & Marcel Nutz & Nizar Touzi, 2015. "Complete Duality for Martingale Optimal Transport on the Line," Papers 1507.00671, arXiv.org, revised Jun 2016.
    2. Sebastian Herrmann & Florian Stebegg, 2017. "Robust Pricing and Hedging around the Globe," Papers 1707.08545, arXiv.org, revised Apr 2019.
    3. Arash Fahim & Yu-Jui Huang & Saeed Khalili, 2019. "Generalized Duality for Model-Free Superhedging given Marginals," Papers 1909.06036, arXiv.org, revised Sep 2019.
    4. Erhan Bayraktar & Shuoqing Deng & Dominykas Norgilas, 2023. "Supermartingale Brenier’s Theorem with Full-Marginal Constraint," World Scientific Book Chapters, in: Robert A Jarrow & Dilip B Madan (ed.), Peter Carr Gedenkschrift Research Advances in Mathematical Finance, chapter 17, pages 569-636, World Scientific Publishing Co. Pte. Ltd..
    5. Yan Dolinsky & Or Zuk, 2023. "Explicit Computations for Delayed Semistatic Hedging," Papers 2308.10550, arXiv.org.
    6. Mathias Beiglbock & Marcel Nutz & Florian Stebegg, 2019. "Fine Properties of the Optimal Skorokhod Embedding Problem," Papers 1903.03887, arXiv.org, revised Apr 2020.
    7. Henry-Labordère, Pierre & Tan, Xiaolu & Touzi, Nizar, 2016. "An explicit martingale version of the one-dimensional Brenier’s Theorem with full marginals constraint," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2800-2834.
    8. Acciaio, Beatrice & Larsson, Martin, 2017. "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.
    9. Zhaoxu Hou & Jan Obłój, 2018. "Robust pricing–hedging dualities in continuous time," Finance and Stochastics, Springer, vol. 22(3), pages 511-567, July.
    10. Marcel Nutz & Florian Stebegg, 2016. "Canonical Supermartingale Couplings," Papers 1609.02867, arXiv.org, revised Nov 2017.

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    More about this item

    Keywords

    Model-independent pricing; Robust superhedging; Limit order book; Fundamental theorem of asset pricing; Portfolio constraints; Monge–Kantorovich optimal transport; 91G20; 91G80; C61; G13;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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