IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1408.5510.html
   My bibliography  Save this paper

Consistent Price Systems under Model Uncertainty

Author

Listed:
  • Bruno Bouchard
  • Marcel Nutz

Abstract

We develop a version of the fundamental theorem of asset pricing for discrete-time markets with proportional transaction costs and model uncertainty. A robust notion of no-arbitrage of the second kind is defined and shown to be equivalent to the existence of a collection of strictly consistent price systems.

Suggested Citation

  • Bruno Bouchard & Marcel Nutz, 2014. "Consistent Price Systems under Model Uncertainty," Papers 1408.5510, arXiv.org.
  • Handle: RePEc:arx:papers:1408.5510
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1408.5510
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bruno Bouchard & Erik Taflin, 2010. "No-arbitrage of second kind in countable markets with proportional transaction costs," Papers 1008.3276, arXiv.org, revised Feb 2013.
    2. Frank Riedel, 2011. "Finance Without Probabilistic Prior Assumptions," Papers 1107.1078, arXiv.org.
    3. Nutz, Marcel & van Handel, Ramon, 2013. "Constructing sublinear expectations on path space," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3100-3121.
    4. 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.
    5. Mark H. A. Davis & David G. Hobson, 2007. "The Range Of Traded Option Prices," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 1-14, January.
    6. Marcel Nutz & Ramon van Handel, 2012. "Constructing Sublinear Expectations on Path Space," Papers 1205.2415, arXiv.org, revised Apr 2013.
    7. (**), Christophe Stricker & (*), Miklós Rásonyi & Yuri Kabanov, 2002. "No-arbitrage criteria for financial markets with efficient friction," Finance and Stochastics, Springer, vol. 6(3), pages 371-382.
    8. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2014. "Universal Arbitrage Aggregator in Discrete Time Markets under Uncertainty," Papers 1407.0948, arXiv.org, revised Feb 2015.
    9. Kabanov, Yu. M. & Stricker, Ch., 2001. "The Harrison-Pliska arbitrage pricing theorem under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 185-196, April.
    10. Yan Dolinsky & H. Soner, 2014. "Robust hedging with proportional transaction costs," Finance and Stochastics, Springer, vol. 18(2), pages 327-347, April.
    11. Erhan Bayraktar & Yuchong Zhang, 2013. "Fundamental Theorem of Asset Pricing under Transaction costs and Model uncertainty," Papers 1309.1420, arXiv.org, revised Aug 2015.
    12. Beatrice Acciaio & Mathias Beiglbock & Friedrich Penkner & Walter Schachermayer, 2013. "A model-free version of the fundamental theorem of asset pricing and the super-replication theorem," Papers 1301.5568, arXiv.org, revised Mar 2013.
    13. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, February.
    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. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2014. "Robust Fundamental Theorem for Continuous Processes," Papers 1410.4962, arXiv.org, revised Jul 2015.
    2. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2017. "Robust Fundamental Theorem for Continuous Processes," Post-Print hal-01076062, HAL.
    3. Yan Dolinsky & H. Mete Soner, 2015. "Convex duality with transaction costs," Papers 1502.01735, arXiv.org, revised Oct 2015.

    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. Bruno Bouchard & Marcel Nutz, 2016. "Consistent price systems under model uncertainty," Finance and Stochastics, Springer, vol. 20(1), pages 83-98, January.
    2. Bruno Bouchard & Marcel Nutz, 2016. "Consistent price systems under model uncertainty," Finance and Stochastics, Springer, vol. 20(1), pages 83-98, January.
    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. Erhan Bayraktar & Yuchong Zhang, 2016. "Fundamental Theorem of Asset Pricing Under Transaction Costs and Model Uncertainty," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 1039-1054, August.
    6. Erhan Bayraktar & Yuchong Zhang & Zhou Zhou, 2014. "A Note on the Fundamental Theorem of Asset Pricing under Model Uncertainty," Risks, MDPI, vol. 2(4), pages 1-9, October.
    7. Nutz, Marcel, 2015. "Robust superhedging with jumps and diffusion," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4543-4555.
    8. Matteo Burzoni & Mario Sikic, 2018. "Robust martingale selection problem and its connections to the no-arbitrage theory," Papers 1801.03574, arXiv.org, revised Nov 2018.
    9. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2016. "Universal arbitrage aggregator in discrete-time markets under uncertainty," Finance and Stochastics, Springer, vol. 20(1), pages 1-50, January.
    10. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2016. "Universal arbitrage aggregator in discrete-time markets under uncertainty," Finance and Stochastics, Springer, vol. 20(1), pages 1-50, January.
    11. Marcel Nutz, 2014. "Robust Superhedging with Jumps and Diffusion," Papers 1407.1674, arXiv.org, revised Jul 2015.
    12. Daniel Bartl, 2016. "Conditional nonlinear expectations," Papers 1612.09103, arXiv.org, revised Mar 2019.
    13. Romain Blanchard & Laurence Carassus, 2021. "Convergence of utility indifference prices to the superreplication price in a multiple‐priors framework," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 366-398, January.
    14. Marcel Nutz, 2013. "Utility Maximization under Model Uncertainty in Discrete Time," Papers 1307.3597, arXiv.org.
    15. Emmanuel Denis & Yuri Kabanov, 2012. "Consistent price systems and arbitrage opportunities of the second kind in models with transaction costs," Finance and Stochastics, Springer, vol. 16(1), pages 135-154, January.
    16. 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.
    17. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2015. "Model-free Superhedging Duality," Papers 1506.06608, arXiv.org, revised May 2016.
    18. Martin Brown & Tomasz Zastawniak, 2020. "Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs," Annals of Finance, Springer, vol. 16(3), pages 423-433, September.
    19. Stefan Gerhold & I. Cetin Gulum, 2016. "Consistency of option prices under bid-ask spreads," Papers 1608.05585, arXiv.org, revised Jul 2019.
    20. Felix-Benedikt Liebrich & Marco Maggis & Gregor Svindland, 2020. "Model Uncertainty: A Reverse Approach," Papers 2004.06636, arXiv.org, revised Mar 2022.

    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:1408.5510. 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.