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Fluid-Limits of Fragmented Limit-Order Markets

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  • 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
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    References listed on IDEAS

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    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.
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