IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2608.30558.html

A note on markets with semi-static trading strategies

Author

Listed:
  • Mikl'os R'asonyi

Abstract

We consider a discrete-time financial market model where, in addition to finitely many dynamically traded assets, there are also (possibly infinitely many) static options to choose from. We introduce the concept of small cones of random variables and present a sufficient condition for the attainable positions in the market to be closed in probability. A fundamental theorem of asset pricing is shown in the present context. Utility maximization will also be considered. We will provide economically meaningful examples of infinite dimensional small cones to demonstrate the pertinence of our approach.

Suggested Citation

  • Mikl'os R'asonyi, 2026. "A note on markets with semi-static trading strategies," Papers 2608.30558, arXiv.org, revised Sep 2026.
    • Handle: RePEc:arx:papers:2608.30558
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2608.30558
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Beatrice Acciaio & Martin Larsson & Walter Schachermayer, 2017. "The space of outcomes of semi-static trading strategies need not be closed," Finance and Stochastics, Springer, vol. 21(3), pages 741-751, July.
    2. Alfred Galichon & Pierre Henri-Labordère & Nizar Touzi, 2014. "A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options," SciencePo Working papers hal-03460952, HAL.
    3. Miklós Rásonyi, 2003. "Equivalent martingale measures for large financial markets in discrete time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(3), pages 401-415, December.
    4. Alfred Galichon & Pierre Henri-Labordère & Nizar Touzi, 2014. "A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options," Sciences Po Economics Publications (main) hal-03460952, HAL.
    5. Alfred Galichon & Pierre Henri-Labordère & Nizar Touzi, 2014. "A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options," Post-Print hal-03460952, HAL.
    6. Freddy Delbaen & Walter Schachermayer, 2006. "The Mathematics of Arbitrage," Springer Finance, Springer, number 978-3-540-31299-4, February.
    7. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    8. 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.
    9. A. Galichon & P. Henry-Labord`ere & N. Touzi, 2014. "A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options," Papers 1401.3921, arXiv.org.
    10. David Hobson & Martin Klimmek, 2012. "Model-independent hedging strategies for variance swaps," Finance and Stochastics, Springer, vol. 16(4), pages 611-649, October.
    11. Acciaio, Beatrice & Larsson, Martin & Schachermayer, Walter, 2017. "The space of outcomes of semi-static trading strategies need not be closed," LSE Research Online Documents on Economics 69804, London School of Economics and Political Science, LSE Library.
    12. J. Jacod & A.N. Shiryaev, 1998. "Local martingales and the fundamental asset pricing theorems in the discrete-time case," Finance and Stochastics, Springer, vol. 2(3), pages 259-273.
    13. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    Full references (including those not matched with items on IDEAS)

    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. Marcel Nutz & Johannes Wiesel & Long Zhao, 2023. "Martingale Schrödinger bridges and optimal semistatic portfolios," Finance and Stochastics, Springer, vol. 27(1), pages 233-254, January.
    2. 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.
    3. Marcel Nutz & Johannes Wiesel & Long Zhao, 2023. "Limits of semistatic trading strategies," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 185-205, January.
    4. Bryan Liang & Marcel Nutz & Shunan Sheng & Valentin Tissot-Daguette, 2026. "Bid--Ask Martingale Optimal Transport," Papers 2603.24605, arXiv.org, revised Sep 2026.
    5. Francesca Biagini & Alessandro Doldi & Jean-Pierre Fouque & Marco Frittelli & Thilo Meyer-Brandis, 2026. "Collective arbitrage and the value of cooperation," Finance and Stochastics, Springer, vol. 30(1), pages 1-57, January.
    6. Marcel Nutz & Johannes Wiesel & Long Zhao, 2022. "Martingale Schr\"odinger Bridges and Optimal Semistatic Portfolios," Papers 2204.12250, arXiv.org.
    7. Julio Backhoff & Gudmund Pammer & Walter Schachermayer, 2025. "The $$L^2$$ L 2 gradient flow of the Bass functional in martingale optimal transport," Mathematics and Financial Economics, Springer, volume 19, number 2, June.
    8. Huy N. Chau & Masaaki Fukasawa & Miklós Rásonyi, 2022. "Super‐replication with transaction costs under model uncertainty for continuous processes," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1066-1085, October.
    9. Alessandro Doldi & Marco Frittelli, 2023. "Entropy martingale optimal transport and nonlinear pricing–hedging duality," Finance and Stochastics, Springer, vol. 27(2), pages 255-304, April.
    10. Mario Ghossoub & Jesse Hall & David Saunders, 2023. "Maximum Spectral Measures of Risk with Given Risk Factor Marginal Distributions," Mathematics of Operations Research, INFORMS, vol. 48(2), pages 1158-1182, May.
    11. Benjamin Jourdain & Gudmund Pammer, 2023. "An extension of martingale transport and stability in robust finance," Papers 2304.09551, arXiv.org.
    12. Mathias Beiglbock & Marcel Nutz & Florian Stebegg, 2019. "Fine Properties of the Optimal Skorokhod Embedding Problem," Papers 1903.03887, arXiv.org, revised Apr 2020.
    13. Acciaio, Beatrice & Larsson, Martin & Schachermayer, Walter, 2017. "The space of outcomes of semi-static trading strategies need not be closed," LSE Research Online Documents on Economics 69804, London School of Economics and Political Science, LSE Library.
    14. Alexander M. G. Cox & Annemarie M. Grass, 2023. "Robust option pricing with volatility term structure -- An empirical study for variance options," Papers 2312.09201, arXiv.org.
    15. Shuoqing Deng & Xin Zhang, 2026. "Distribution-constrained maximum stopping of maximum type," Papers 2610.01585, arXiv.org.
    16. 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.
    17. Gaoyue Guo & Xiaolu Tan & Nizar Touzi, 2016. "Optimal Skorokhod embedding under finitely-many marginal constraints," Post-Print hal-01247004, HAL.
    18. Shuoqing Deng & Daxin Huang, 2026. "Distribution-constrained optimal multiple stopping: the Root-type solution," Papers 2608.27374, arXiv.org, revised Sep 2026.
    19. Marcel Nutz & Johannes Wiesel & Long Zhao, 2022. "Limits of Semistatic Trading Strategies," Papers 2204.12251, arXiv.org.
    20. Purba Banerjee & Srikanth Iyer & Shashi Jain, 2025. "Robust Hedging of path-dependent options using a min-max algorithm," Papers 2511.00781, arXiv.org.

    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:2608.30558. 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: https://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.