IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1502.01735.html
   My bibliography  Save this paper

Convex duality with transaction costs

Author

Listed:
  • Yan Dolinsky
  • H. Mete Soner

Abstract

Convex duality for two two different super--replication problems in a continuous time financial market with proportional transaction cost is proved. In this market, static hedging in a finite number of options, in addition to usual dynamic hedging with the underlying stock, are allowed. The first one the problems considered is the model--independent hedging that requires the super--replication to hold for every continuous path. In the second one the market model is given through a probability measure P and the inequalities are understood P almost surely. The main result, using the convex duality, proves that the two super--replication problems have the same value provided that P satisfies the conditional full support property. Hence, the transaction costs prevents one from using the structure of a specific model to reduce the super--replication cost.

Suggested Citation

  • Yan Dolinsky & H. Mete Soner, 2015. "Convex duality with transaction costs," Papers 1502.01735, arXiv.org, revised Oct 2015.
    • Handle: RePEc:arx:papers:1502.01735
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1502.01735
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mathias Beiglbock & 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.
    2. Walter Schachermayer, 2004. "The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 19-48, January.
    3. Walter Schachermayer, 2014. "The super-replication theorem under proportional transaction costs revisited," Papers 1405.1266, arXiv.org.
    4. Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 15-35, March.
    5. 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.
    6. Yan Dolinsky & H. Soner, 2014. "Robust hedging with proportional transaction costs," Finance and Stochastics, Springer, vol. 18(2), pages 327-347, April.
    7. Paolo Guasoni & Mikl'os R'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
    8. repec:dau:papers:123456789/1533 is not listed on IDEAS
    9. Mathias Beiglböck & Pierre Henry-Labordère & Friedrich Penkner, 2013. "Model-independent bounds for option prices—a mass transport approach," Finance and Stochastics, Springer, vol. 17(3), pages 477-501, July.
    10. Bruno Bouchard & Marcel Nutz, 2014. "Consistent Price Systems under Model Uncertainty," Papers 1408.5510, arXiv.org.
    11. Yan DOLINSKY & Mete SONER, 2014. "Martingale Optimal Transport in the Skorokhod Space," Swiss Finance Institute Research Paper Series 14-62, Swiss Finance Institute.
    12. Erhan Bayraktar & Yuchong Zhang, 2013. "Fundamental Theorem of Asset Pricing under Transaction costs and Model uncertainty," Papers 1309.1420, arXiv.org, revised Aug 2015.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Matteo Burzoni, 2015. "Arbitrage and Hedging in model-independent markets with frictions," Papers 1512.01488, arXiv.org, revised Aug 2016.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yan Dolinsky & H. Mete Soner, 2017. "Convex Duality with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 448-471, May.
    2. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2015. "Model-free Superhedging Duality," Papers 1506.06608, arXiv.org, revised May 2016.
    3. Matteo Burzoni, 2015. "Arbitrage and Hedging in model-independent markets with frictions," Papers 1512.01488, arXiv.org, revised Aug 2016.
    4. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2014. "Robust Fundamental Theorem for Continuous Processes," Papers 1410.4962, arXiv.org, revised Jul 2015.
    5. Sergey Badikov & Mark H. A. Davis & Antoine Jacquier, 2018. "Perturbation analysis of sub/super hedging problems," Papers 1806.03543, arXiv.org, revised May 2021.
    6. Erhan Bayraktar & Yu-Jui Huang & Zhou Zhou, 2013. "On hedging American options under model uncertainty," Papers 1309.2982, arXiv.org, revised Apr 2015.
    7. Mathias Beiglbock & Alexander M. G. Cox & Martin Huesmann & Nicolas Perkowski & David J. Promel, 2015. "Pathwise super-replication via Vovk's outer measure," Papers 1504.03644, arXiv.org, revised Jul 2016.
    8. Anna Aksamit & Zhaoxu Hou & Jan Obl'oj, 2016. "Robust framework for quantifying the value of information in pricing and hedging," Papers 1605.02539, arXiv.org, revised Mar 2018.
    9. Cox, Alexander M.G. & Kinsley, Sam M., 2019. "Discretisation and duality of optimal Skorokhod embedding problems," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2376-2405.
    10. Arash Fahim & Yu-Jui Huang, 2016. "Model-independent superhedging under portfolio constraints," Finance and Stochastics, Springer, vol. 20(1), pages 51-81, January.
    11. Arash Fahim & Yu-Jui Huang, 2014. "Model-independent Superhedging under Portfolio Constraints," Papers 1402.2599, arXiv.org, revised Jun 2015.
    12. Bruno Bouchard & Marcel Nutz, 2014. "Consistent Price Systems under Model Uncertainty," Papers 1408.5510, arXiv.org.
    13. Yan Dolinsky & H. Soner, 2014. "Robust hedging with proportional transaction costs," Finance and Stochastics, Springer, vol. 18(2), pages 327-347, April.
    14. Stephan Eckstein & Michael Kupper, 2019. "Martingale transport with homogeneous stock movements," Papers 1908.10242, arXiv.org, revised May 2021.
    15. Paolo Guasoni & Miklós Rásonyi & Walter Schachermayer, 2010. "The fundamental theorem of asset pricing for continuous processes under small transaction costs," Annals of Finance, Springer, vol. 6(2), pages 157-191, March.
    16. Patrick Cheridito & Matti Kiiski & David J. Promel & H. Mete Soner, 2019. "Martingale optimal transport duality," Papers 1904.04644, arXiv.org, revised Nov 2020.
    17. Daniel Krv{s}ek & Gudmund Pammer, 2024. "General duality and dual attainment for adapted transport," Papers 2401.11958, arXiv.org, revised Nov 2024.
    18. Matteo Burzoni & Marco Frittelli & Zhaoxu Hou & Marco Maggis & Jan Obłój, 2019. "Pointwise Arbitrage Pricing Theory in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 1034-1057, August.
    19. Yiqing Lin & Junjian Yang, 2016. "Utility maximization problem with random endowment and transaction costs: when wealth may become negative," Papers 1604.08224, arXiv.org, revised Sep 2016.
    20. Zhaoxu Hou & Jan Obłój, 2018. "Robust pricing–hedging dualities in continuous time," Finance and Stochastics, Springer, vol. 22(3), pages 511-567, July.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1502.01735. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.