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Super-replication with transaction costs under model uncertainty for continuous processes

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  • Huy N. Chau
  • Masaaki Fukasawa
  • Miklos Rasonyi

Abstract

We formulate a superhedging theorem in the presence of transaction costs and model uncertainty. Asset prices are assumed continuous and uncertainty is modelled in a parametric setting. Our proof relies on a new topological framework in which no Krein-Smulian type theorem is available.

Suggested Citation

  • Huy N. Chau & Masaaki Fukasawa & Miklos Rasonyi, 2021. "Super-replication with transaction costs under model uncertainty for continuous processes," Papers 2102.02298, arXiv.org.
    • Handle: RePEc:arx:papers:2102.02298
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    References listed on IDEAS

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    1. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2017. "Robust Fundamental Theorem for Continuous Processes," Post-Print hal-01076062, HAL.
    2. repec:dau:papers:123456789/9300 is not listed on IDEAS
    3. Wen Li & Song Wang, 2014. "A numerical method for pricing European options with proportional transaction costs," Journal of Global Optimization, Springer, vol. 60(1), pages 59-78, September.
    4. Alexander Cox & Jan Obłój, 2011. "Robust pricing and hedging of double no-touch options," Finance and Stochastics, Springer, vol. 15(3), pages 573-605, September.
    5. Marcel Nutz, 2014. "Superreplication under model uncertainty in discrete time," Finance and Stochastics, Springer, vol. 18(4), pages 791-803, October.
    6. Yuri M. Kabanov & Günter Last, 2002. "Hedging under Transaction Costs in Currency Markets: a Continuous‐Time Model," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 63-70, January.
    7. Huy N. Chau & Miklós Rásonyi, 2019. "Robust utility maximisation in markets with transaction costs," Finance and Stochastics, Springer, vol. 23(3), pages 677-696, July.
    8. Paolo Guasoni & Emmanuel Lépinette & Miklós Rásonyi, 2012. "The fundamental theorem of asset pricing under transaction costs," Finance and Stochastics, Springer, vol. 16(4), pages 741-777, October.
    9. Daniel Bartl & Michael Kupper & David J. Promel & Ludovic Tangpi, 2017. "Duality for pathwise superhedging in continuous time," Papers 1705.02933, arXiv.org, revised Apr 2019.
    10. Patrick Cheridito & Matti Kiiski & David J. Promel & H. Mete Soner, 2019. "Martingale optimal transport duality," Papers 1904.04644, arXiv.org, revised Nov 2020.
    11. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    12. 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.
    13. Mikl'os R'asonyi & Andrea Meireles-Rodrigues, 2018. "On Utility Maximisation Under Model Uncertainty in Discrete-Time Markets," Papers 1801.06860, arXiv.org, revised Jul 2020.
    14. Mark Davis & Jan Obłój & Vimal Raval, 2014. "Arbitrage Bounds For Prices Of Weighted Variance Swaps," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 821-854, October.
    15. W. Schachermayer, 1994. "Martingale Measures For Discrete‐Time Processes With Infinite Horizon," Mathematical Finance, Wiley Blackwell, vol. 4(1), pages 25-55, January.
    16. Marco Maggis & Thilo Meyer-Brandis & Gregor Svindland, 2016. "The Fatou Closedness under Model Uncertainty," Papers 1610.04085, arXiv.org, revised Oct 2018.
    17. Patrick Cheridito & Michael Kupper & Ludovic Tangpi, 2016. "Duality formulas for robust pricing and hedging in discrete time," Papers 1602.06177, arXiv.org, revised Sep 2017.
    18. Yuri Kabanov, 2009. "Markets with Transaction Costs. Mathematical Theory," Post-Print hal-00488168, HAL.
    19. Haydyn Brown & David Hobson & L. C. G. Rogers, 2001. "Robust Hedging of Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 11(3), pages 285-314, July.
    20. Peter Carr & Roger Lee, 2010. "Hedging variance options on continuous semimartingales," Finance and Stochastics, Springer, vol. 14(2), pages 179-207, April.
    21. Alfred Galichon & Pierre Henri-Labordère & Nizar Touzi, 2013. "A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
    22. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
    23. Walter Schachermayer, 2013. "Admissible Trading Strategies under Transaction Costs," Papers 1308.1492, arXiv.org, revised May 2014.
    24. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2017. "Robust Fundamental Theorem For Continuous Processes," Mathematical Finance, Wiley Blackwell, vol. 27(4), pages 963-987, October.
    25. B. Acciaio & M. Beiglböck & F. Penkner & W. Schachermayer, 2016. "A Model-Free Version Of The Fundamental Theorem Of Asset Pricing And The Super-Replication Theorem," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 233-251, April.
    26. Yan Dolinsky & H. Soner, 2014. "Robust hedging with proportional transaction costs," Finance and Stochastics, Springer, vol. 18(2), pages 327-347, April.
    27. Marcel Nutz, 2013. "Superreplication under Model Uncertainty in Discrete Time," Papers 1301.3227, arXiv.org, revised Feb 2014.
    28. Bruno Bouchard & Shuoqing Deng & Xiaolu Tan, 2019. "Superreplication with proportional transaction cost under model uncertainty," Mathematical Finance, Wiley Blackwell, vol. 29(3), pages 837-860, July.
    29. Daniel Bartl & Michael Kupper & David J. Prömel & Ludovic Tangpi, 2019. "Duality for pathwise superhedging in continuous time," Finance and Stochastics, Springer, vol. 23(3), pages 697-728, July.
    30. Huy N. Chau, 2020. "On robust fundamental theorems of asset pricing in discrete time," Papers 2007.02553, arXiv.org, revised Apr 2024.
    31. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
    32. Zhaoxu Hou & Jan Obłój, 2018. "Robust pricing–hedging dualities in continuous time," Finance and Stochastics, Springer, vol. 22(3), pages 511-567, July.
    33. Yan Dolinsky & H. Mete Soner, 2017. "Convex Duality with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 448-471, May.
    34. 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.
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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.

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