Fluid-Limits of Fragmented Limit-Order Markets
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914859566759936 |
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| author | Muhle-Karbe, Johannes Neuman, Eyal Shadmi, Yonatan |
| author_facet | Muhle-Karbe, Johannes Neuman, Eyal Shadmi, Yonatan |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04354 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fluid-Limits of Fragmented Limit-Order Markets Muhle-Karbe, Johannes Neuman, Eyal Shadmi, Yonatan Probability Mathematical Finance 60K25, 90B22, 37A50 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). |
| title | Fluid-Limits of Fragmented Limit-Order Markets |
| topic | Probability Mathematical Finance 60K25, 90B22, 37A50 |
| url | https://arxiv.org/abs/2407.04354 |