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Pathwise superhedging on prediction sets

Author

Listed:
  • Daniel Bartl

    (University of Vienna)

  • Michael Kupper

    (University of Konstanz)

  • Ariel Neufeld

    (NTU Singapore)

Abstract

In this paper, we provide a pricing–hedging duality for the model-independent superhedging price with respect to a prediction set Ξ⊆C[0,T]$\Xi \subseteq C[0,T]$, where the superhedging property needs to hold pathwise, but only for paths lying in Ξ$\Xi $. For any Borel-measurable claim ξ$\xi $ bounded from below, the superhedging price coincides with the supremum over all pricing functionals EQ[ξ]$\mathbb{E}_{\mathbb{Q}}[ \xi ]$ with respect to martingale measures ℚ concentrated on the prediction set Ξ$\Xi $. This allows us to include beliefs about future paths of the price process expressed by the set Ξ$\Xi $, while eliminating all those which are seen as impossible. Moreover, we provide several examples to justify our setup.

Suggested Citation

  • Daniel Bartl & Michael Kupper & Ariel Neufeld, 2020. "Pathwise superhedging on prediction sets," Finance and Stochastics, Springer, vol. 24(1), pages 215-248, January.
    • Handle: RePEc:spr:finsto:v:24:y:2020:i:1:d:10.1007_s00780-019-00412-4
    DOI: 10.1007/s00780-019-00412-4
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Felix-Benedikt Liebrich & Marco Maggis & Gregor Svindland, 2020. "Model Uncertainty: A Reverse Approach," Papers 2004.06636, arXiv.org, revised Mar 2022.
    2. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2021. "Duality theory for robust utility maximisation," Finance and Stochastics, Springer, vol. 25(3), pages 469-503, July.
    3. Francesca Biagini & Thomas Reitsam, 2021. "A dynamic version of the super-replication theorem under proportional transaction costs," Papers 2107.02628, arXiv.org.
    4. Francesca Biagini & Lukas Gonon & Thomas Reitsam, 2023. "Neural network approximation for superhedging prices," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 146-184, January.
    5. Jonathan Ansari & Eva Lutkebohmert & Ariel Neufeld & Julian Sester, 2022. "Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information," Papers 2204.01071, arXiv.org, revised Sep 2023.
    6. Christian Bender & Sebastian Ferrando & Alfredo Gonzalez, 2021. "Model-Free Finance and Non-Lattice Integration," Papers 2105.10623, arXiv.org.
    7. Julian Sester, 2023. "On intermediate Marginals in Martingale Optimal Transportation," Papers 2307.09710, arXiv.org, revised Nov 2023.
    8. Ariel Neufeld & Julian Sester, 2021. "Model-free price bounds under dynamic option trading," Papers 2101.01024, arXiv.org, revised Jul 2021.
    9. Jonathan Ansari & Eva Lütkebohmert & Ariel Neufeld & Julian Sester, 2024. "Improved robust price bounds for multi-asset derivatives under market-implied dependence information," Finance and Stochastics, Springer, vol. 28(4), pages 911-964, October.
    10. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2020. "Duality Theory for Robust Utility Maximisation," Papers 2007.08376, arXiv.org, revised Jun 2021.
    11. Rafa{l} M. {L}ochowski & Nicolas Perkowski & David J. Promel, 2021. "One-dimensional game-theoretic differential equations," Papers 2101.08041, arXiv.org.
    12. Ariel Neufeld & Antonis Papapantoleon & Qikun Xiang, 2020. "Model-free bounds for multi-asset options using option-implied information and their exact computation," Papers 2006.14288, arXiv.org, revised Jan 2022.
    13. Ariel Neufeld & Antonis Papapantoleon & Qikun Xiang, 2023. "Model-Free Bounds for Multi-Asset Options Using Option-Implied Information and Their Exact Computation," Management Science, INFORMS, vol. 69(4), pages 2051-2068, April.
    14. Francesca Biagini & Lukas Gonon & Thomas Reitsam, 2021. "Neural network approximation for superhedging prices," Papers 2107.14113, arXiv.org.

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    More about this item

    Keywords

    Model-independent superhedging; Pricing–hedging duality; Modelling beliefs;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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