IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2407.04354.html
   My bibliography  Save this paper

Fluid-Limits of Fragmented Limit-Order Markets

Author

Listed:
  • Johannes Muhle-Karbe
  • Eyal Neuman
  • Yonatan Shadmi

Abstract

Maglaras, Moallemi, and Zheng (2021) have introduced a flexible queueing model for fragmented limit-order markets, whose fluid limit remains remarkably tractable. In the present study we prove that, in the limit of small and frequent orders, the discrete system indeed converges to the fluid limit, which is characterized by a system of coupled nonlinear ODEs with singular coefficients at the origin. Moreover, we establish that the fluid system is asymptotically stable for an arbitrary number of limit order books in that, over time, it converges to the stationary equilibrium state studied by Maglaras et al. (2021).

Suggested Citation

  • Johannes Muhle-Karbe & Eyal Neuman & Yonatan Shadmi, 2024. "Fluid-Limits of Fragmented Limit-Order Markets," Papers 2407.04354, arXiv.org.
    • Handle: RePEc:arx:papers:2407.04354
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2407.04354
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Baldauf, Markus & Mollner, Joshua, 2021. "Trading in Fragmented Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 56(1), pages 93-121, February.
    2. Avishai Mandelbaum & Alexander L. Stolyar, 2004. "Scheduling Flexible Servers with Convex Delay Costs: Heavy-Traffic Optimality of the Generalized cμ-Rule," Operations Research, INFORMS, vol. 52(6), pages 836-855, December.
    3. Omar El Euch & Thibaut Mastrolia & Mathieu Rosenbaum & Nizar Touzi, 2021. "Optimal make–take fees for market making regulation," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 109-148, January.
    4. Rama Cont & Arseniy Kukanov, 2017. "Optimal order placement in limit order markets," Quantitative Finance, Taylor & Francis Journals, vol. 17(1), pages 21-39, January.
    5. Ben Hambly & Jasdeep Kalsi & James Newbury, 2020. "Limit Order Books, Diffusion Approximations and Reflected SPDEs: From Microscopic to Macroscopic Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(1-2), pages 132-170, July.
    6. Cassandra Milbradt & Dorte Kreher, 2022. "A cross-border market model with limited transmission capacities," Papers 2207.01939, arXiv.org, revised May 2023.
    7. Frank Kelly & Elena Yudovina, 2018. "A Markov Model of a Limit Order Book: Thresholds, Recurrence, and Trading Strategies," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 181-203, February.
    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. Konark Jain & Nick Firoozye & Jonathan Kochems & Philip Treleaven, 2024. "Limit Order Book Simulations: A Review," Papers 2402.17359, arXiv.org, revised Mar 2024.
    2. Amy R. Ward & Mor Armony, 2013. "Blind Fair Routing in Large-Scale Service Systems with Heterogeneous Customers and Servers," Operations Research, INFORMS, vol. 61(1), pages 228-243, February.
    3. Achal Bassamboo & J. Michael Harrison & Assaf Zeevi, 2006. "Design and Control of a Large Call Center: Asymptotic Analysis of an LP-Based Method," Operations Research, INFORMS, vol. 54(3), pages 419-435, June.
    4. Babus, Ana & Parlatore, Cecilia, 2022. "Strategic fragmented markets," Journal of Financial Economics, Elsevier, vol. 145(3), pages 876-908.
    5. Gabriel Zayas‐Cabán & Emmett J. Lodree & David L. Kaufman, 2020. "Optimal Control of Parallel Queues for Managing Volunteer Convergence," Production and Operations Management, Production and Operations Management Society, vol. 29(10), pages 2268-2288, October.
    6. Philippe Bergault & Enzo Cogn'eville, 2024. "Simulating and analyzing a sparse order book: an application to intraday electricity markets," Papers 2410.06839, arXiv.org.
    7. Kuang Xu & Yuan Zhong, 2020. "Information and Memory in Dynamic Resource Allocation," Operations Research, INFORMS, vol. 68(6), pages 1698-1715, November.
    8. Wanyang Dai, 2013. "Optimal Rate Scheduling via Utility-Maximization for J -User MIMO Markov Fading Wireless Channels with Cooperation," Operations Research, INFORMS, vol. 61(6), pages 1450-1462, December.
    9. Rami Atar & Subhamay Saha, 2017. "Optimality of the generalized $$\varvec{c\mu }$$ c μ rule in the moderate deviation regime," Queueing Systems: Theory and Applications, Springer, vol. 87(1), pages 113-130, October.
    10. Bastien Baldacci & Jerome Benveniste & Gordon Ritter, 2020. "Optimal trading without optimal control," Papers 2012.12945, arXiv.org.
    11. Gregory Dobson & Tolga Tezcan & Vera Tilson, 2013. "Optimal Workflow Decisions for Investigators in Systems with Interruptions," Management Science, INFORMS, vol. 59(5), pages 1125-1141, May.
    12. Merve Bodur & James R. Luedtke, 2017. "Mixed-Integer Rounding Enhanced Benders Decomposition for Multiclass Service-System Staffing and Scheduling with Arrival Rate Uncertainty," Management Science, INFORMS, vol. 63(7), pages 2073-2091, July.
    13. Ben Hambly & Renyuan Xu & Huining Yang, 2021. "Recent Advances in Reinforcement Learning in Finance," Papers 2112.04553, arXiv.org, revised Feb 2023.
    14. Cassandra Milbradt & Dorte Kreher, 2022. "A cross-border market model with limited transmission capacities," Papers 2207.01939, arXiv.org, revised May 2023.
    15. Rami Atar & Avi Mandelbaum & Gennady Shaikhet, 2009. "Simplified Control Problems for Multiclass Many-Server Queueing Systems," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 795-812, November.
    16. Schnaubelt, Matthias, 2022. "Deep reinforcement learning for the optimal placement of cryptocurrency limit orders," European Journal of Operational Research, Elsevier, vol. 296(3), pages 993-1006.
    17. J. G. Dai & Tolga Tezcan, 2011. "State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 271-320, May.
    18. Xianfei Hui & Baiqing Sun & Hui Jiang & Indranil SenGupta, 2021. "Analysis of stock index with a generalized BN-S model: an approach based on machine learning and fuzzy parameters," Papers 2101.08984, arXiv.org, revised Feb 2022.
    19. Sigrún Andradóttir & Hayriye Ayhan & Douglas G. Down, 2007. "Compensating for Failures with Flexible Servers," Operations Research, INFORMS, vol. 55(4), pages 753-768, August.
    20. Dylan Possamai & Chiara Rossato, 2023. "Golden parachutes under the threat of accidents," Papers 2312.02101, arXiv.org, revised Sep 2024.

    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:2407.04354. 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.