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Martingale Optimal Transport and Robust Hedging in Continuous Time

Author

Listed:
  • Yan Dolinsky

    (ETH Zürich)

  • Halil Mete Soner

    (ETH Zürich; Swiss Finance Institute)

Abstract

The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only assumed to be a continuous function of time. The hedging problem is to construct a minimal super-hedging portfolio that consists of dynamically trading the underlying risky asset and a static position of vanilla options which can be exercised at the given, fi xed maturity. The dual is a Monge-Kantorovich type martingale transport problem of maximizing the expected value of the option over all martingale measures that has the given marginal at maturity. In addition to duality, a family of simple, piecewise constant super-replication portfolios that asymptotically achieve the minimal super-replication cost is constructed.

Suggested Citation

  • Yan Dolinsky & Halil Mete Soner, 2013. "Martingale Optimal Transport and Robust Hedging in Continuous Time," Swiss Finance Institute Research Paper Series 13-13, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1313
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    File URL: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2245481
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    Citations

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    Cited by:

    1. Erhan Bayraktar & Yu-Jui Huang & Zhou Zhou, 2013. "On hedging American options under model uncertainty," Papers 1309.2982, arXiv.org, revised Apr 2015.
    2. Yan Dolinsky & H. Mete Soner, 2017. "Convex Duality with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 448-471, May.
    3. David Hobson & Martin Klimmek, 2013. "Robust price bounds for the forward starting straddle," Papers 1304.2141, arXiv.org.
    4. Zhaoxu Hou & Jan Obloj, 2015. "On robust pricing-hedging duality in continuous time," Papers 1503.02822, arXiv.org, revised Jul 2015.
    5. Alexander M. G. Cox & Jiajie Wang, 2013. "Optimal robust bounds for variance options," Papers 1308.4363, arXiv.org.
    6. Arash Fahim & Yu-Jui Huang, 2014. "Model-independent Superhedging under Portfolio Constraints," Papers 1402.2599, arXiv.org, revised Jun 2015.
    7. Miklós Rásonyi & Andrea Meireles‐Rodrigues, 2021. "On utility maximization under model uncertainty in discrete‐time markets," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 149-175, January.
    8. Alexander M. G. Cox & Sigrid Kallblad, 2015. "Model-independent bounds for Asian options: a dynamic programming approach," Papers 1507.02651, arXiv.org, revised Jul 2016.
    9. Erhan Bayraktar & Zhou Zhou, 2013. "On model-independent pricing/hedging using shortfall risk and quantiles," Papers 1307.2493, arXiv.org.
    10. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2015. "Model-free Superhedging Duality," Papers 1506.06608, arXiv.org, revised May 2016.
    11. Yan Dolinsky & H. Mete Soner, 2015. "Convex duality with transaction costs," Papers 1502.01735, arXiv.org, revised Oct 2015.

    More about this item

    Keywords

    European Options; Robust Hedging; Min-Max Theorems; Prokhorov Metric; Optimal transport;
    All these keywords.

    JEL classification:

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

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