IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2511.12093.html

On the utility problem in a market where price impact is transient

Author

Listed:
  • L'or'ant Nagy
  • Mikl'os R'asonyi

Abstract

We consider a discrete-time model of a financial market where a risky asset is bought and sold with transactions having a transient price impact. It is shown that the corresponding utility maximization problem admits a solution. We manage to remove some unnatural restrictions on the market depth and resilience processes that were present in earlier work. A non-standard feature of the problem is that the set of attainable portfolio values may fail the convexity property.

Suggested Citation

  • L'or'ant Nagy & Mikl'os R'asonyi, 2025. "On the utility problem in a market where price impact is transient," Papers 2511.12093, arXiv.org.
    • Handle: RePEc:arx:papers:2511.12093
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2511.12093
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Peter Bank & Yan Dolinsky & Mikl'os R'asonyi, 2021. "What if we knew what the future brings? Optimal investment for a frontrunner with price impact," Papers 2108.04291, arXiv.org, revised May 2022.
    2. Miklos Rasonyi & Lukasz Stettner, 2005. "On utility maximization in discrete-time financial market models," Papers math/0505243, arXiv.org.
    3. Laurence Carassus & Miklós Rásonyi, 2016. "Maximization of Nonconcave Utility Functions in Discrete-Time Financial Market Models," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 146-173, February.
    4. Peter Bank & Yan Dolinsky, 2018. "Continuous-time Duality for Super-replication with Transient Price Impact," Papers 1808.09807, arXiv.org, revised May 2019.
    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. Romain Blanchard & Laurence Carassus & Miklós Rásonyi, 2018. "No-arbitrage and optimal investment with possibly non-concave utilities: a measure theoretical approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 241-281, October.
    2. Laurence Carassus & Massinissa Ferhoune, 2024. "Nonconcave Robust Utility Maximization under Projective Determinacy," Papers 2403.11824, arXiv.org, revised Oct 2025.
    3. Laurence Carassus & Massinissa Ferhoune, 2023. "Discrete time optimal investment under model uncertainty," Papers 2307.11919, arXiv.org, revised Feb 2024.
    4. Romain Blanchard & Laurence Carassus & Miklos Rasonyi, 2018. "Optimal investment with possibly non-concave utilities and no-arbitrage: a measure theoretical approach," Post-Print hal-01883419, HAL.
    5. Carassus, Laurence & Ferhoune, Massinissa, 2025. "Discrete time optimal investment under model uncertainty," Stochastic Processes and their Applications, Elsevier, vol. 189(C).
    6. 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.
    7. Miklos Rasonyi, 2015. "Maximizing expected utility in the Arbitrage Pricing Model," Papers 1508.07761, arXiv.org, revised Mar 2017.
    8. Shuoqing Deng & Xiaolu Tan & Xiang Yu, 2020. "Utility Maximization with Proportional Transaction Costs Under Model Uncertainty," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1210-1236, November.
    9. Yan Dolinsky & Shir Moshe, 2021. "Utility Indifference Pricing with High Risk Aversion and Small Linear Price Impact," Papers 2111.00451, arXiv.org, revised Jan 2022.
    10. Fontana, Claudio & Runggaldier, Wolfgang J., 2021. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 66-80.
    11. Martin Herdegen & Nazem Khan, 2020. "Mean-$\rho$ portfolio selection and $\rho$-arbitrage for coherent risk measures," Papers 2009.05498, arXiv.org, revised Jul 2021.
    12. Tahir Choulli & Jun Deng & Junfeng Ma, 2015. "How non-arbitrage, viability and numéraire portfolio are related," Finance and Stochastics, Springer, vol. 19(4), pages 719-741, October.
    13. Ariel Neufeld & Mario Šikić, 2019. "Nonconcave robust optimization with discrete strategies under Knightian uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(2), pages 229-253, October.
    14. Romain Blanchard & Laurence Carassus & Mikl'os R'asonyi, 2016. "Non-concave optimal investment and no-arbitrage: a measure theoretical approach," Papers 1602.06685, arXiv.org, revised Aug 2016.
    15. H'el`ene Halconruy, 2021. "The insider problem in the trinomial model: a discrete-time jump process approach," Papers 2106.15208, arXiv.org, revised Sep 2023.
    16. Roman Muraviev, 2011. "Additive habits with power utility: Estimates, asymptotics and equilibrium," Papers 1108.2889, arXiv.org.
    17. Laurence Carassus & Miklós Rásonyi, 2016. "Maximization of Nonconcave Utility Functions in Discrete-Time Financial Market Models," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 146-173, February.
    18. Nuerxiati Abudurexiti & Erhan Bayraktar & Takaki Hayashi & Hasanjan Sayit, 2024. "Two-fund separation under hyperbolically distributed returns and concave utility functions," Papers 2410.04459, arXiv.org, revised Sep 2025.
    19. Ayelet Amiran & Fabrice Baudoin & Skylyn Brock & Berend Coster & Ryan Craver & Ugonna Ezeaka & Phanuel Mariano & Mary Wishart, 2018. "The financial value of knowing the distribution of stock prices in discrete market models," Papers 1808.03186, arXiv.org.
    20. Claudio Fontana & Wolfgang J. Runggaldier, 2020. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Papers 2006.15563, arXiv.org, revised Sep 2020.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:2511.12093. 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.