IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2504.06717.html
   My bibliography  Save this paper

Optimal Execution and Macroscopic Market Making

Author

Listed:
  • Ivan Guo
  • Shijia Jin

Abstract

We propose a stochastic game modelling the strategic interaction between market makers and traders of optimal execution type. For traders, the permanent price impact commonly attributed to them is replaced by quoting strategies implemented by market makers. For market makers, order flows become endogenous, driven by tactical traders rather than assumed exogenously. Using the forward-backward stochastic differential equation (FBSDE) characterization of Nash equilibria, we establish a local well-posedness result for the general game. In the specific Almgren-Chriss-Avellaneda-Stoikov model, a decoupling approach guarantees the global well-posedness of the FBSDE system via the well-posedness of an associated backward stochastic Riccati equation. Finally, by introducing small diffusion terms into the inventory processes, global well-posedness is achieved for the approximation game.

Suggested Citation

  • Ivan Guo & Shijia Jin, 2025. "Optimal Execution and Macroscopic Market Making," Papers 2504.06717, arXiv.org.
    • Handle: RePEc:arx:papers:2504.06717
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2504.06717
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Alexander Schied & Tao Zhang, 2017. "A State-Constrained Differential Game Arising In Optimal Portfolio Liquidation," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 779-802, July.
    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. Yinhong Dong & Donglei Du & Qiaoming Han & Jianfeng Ren & Dachuan Xu, 2024. "A Stackelberg order execution game," Annals of Operations Research, Springer, vol. 336(1), pages 571-604, May.
    2. Moritz Voß, 2022. "A two-player portfolio tracking game," Mathematics and Financial Economics, Springer, volume 16, number 6, February.
    3. Masaaki Fujii & Akihiko Takahashi, 2021. "A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition," CIRJE F-Series CIRJE-F-1177, CIRJE, Faculty of Economics, University of Tokyo.
    4. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2018. "Optimal liquidation under stochastic liquidity," Finance and Stochastics, Springer, vol. 22(1), pages 39-68, January.
    5. Francesco Cordoni & Fabrizio Lillo, 2020. "Instabilities in Multi-Asset and Multi-Agent Market Impact Games," Papers 2004.03546, arXiv.org, revised Nov 2021.
    6. Alexander Schied & Tao Zhang, 2019. "A Market Impact Game Under Transient Price Impact," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 102-121, February.
    7. Xiangge Luo & Alexander Schied, 2018. "Nash equilibrium for risk-averse investors in a market impact game with transient price impact," Papers 1807.03813, arXiv.org, revised Jun 2019.
    8. Masaaki Fujii & Akihiko Takahashi, 2021. "A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition," CARF F-Series CARF-F-521, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    9. Moritz Vo{ss}, 2019. "A two-player portfolio tracking game," Papers 1911.05122, arXiv.org, revised Jul 2022.
    10. Samuel Drapeau & Peng Luo & Alexander Schied & Dewen Xiong, 2019. "An FBSDE approach to market impact games with stochastic parameters," Papers 2001.00622, arXiv.org.
    11. Francesco Cordoni & Fabrizio Lillo, 2024. "Instabilities in multi-asset and multi-agent market impact games," Annals of Operations Research, Springer, vol. 336(1), pages 505-539, May.
    12. Steven Campbell & Marcel Nutz, 2025. "Optimal Execution among $N$ Traders with Transient Price Impact," Papers 2501.09638, arXiv.org.
    13. Nicole Bäuerle & Tamara Göll, 2024. "Nash equilibria for relative investors with (non)linear price impact," Mathematics and Financial Economics, Springer, volume 18, number 2, February.
    14. Fabrizio Lillo & Andrea Macr`i, 2024. "Deviations from the Nash equilibrium and emergence of tacit collusion in a two-player optimal execution game with reinforcement learning," Papers 2408.11773, arXiv.org.

    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:2504.06717. 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.