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Volume 6, Issue 2
Optimal Strategy for Limit Order Book Submissions in High Frequency Trading

Na Song, Yue Xie, Wai-Ki Ching, Tak-Kuen Siu & Cedric Ka-Fai Yiu

East Asian J. Appl. Math., 6 (2016), pp. 222-234.

Published online: 2018-02

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  • Abstract

An optimal selection problem for bid and ask quotes subject to a stock inventory constraint is investigated, formulated as a constrained utility maximisation problem over a finite time horizon. The arrivals of buy and sell orders are governed by Poisson processes, and a diffusion approximation is employed on assuming the Poisson arrivals intensity is sufficiently large. Using the dynamic programming principle, we adopt an efficient numerical procedure to solve this constrained utility maximisation problem based on a successive approximation algorithm, and conduct numerical experiments to analyse the impacts of the inventory constraint on a dealer’s terminal profit and stock inventory level. It is found that the stock inventory constraint significantly affects the terminal stock inventory level.

  • AMS Subject Headings

60K25, 68M20, 91A80

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-6-222, author = {}, title = {Optimal Strategy for Limit Order Book Submissions in High Frequency Trading}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {6}, number = {2}, pages = {222--234}, abstract = {

An optimal selection problem for bid and ask quotes subject to a stock inventory constraint is investigated, formulated as a constrained utility maximisation problem over a finite time horizon. The arrivals of buy and sell orders are governed by Poisson processes, and a diffusion approximation is employed on assuming the Poisson arrivals intensity is sufficiently large. Using the dynamic programming principle, we adopt an efficient numerical procedure to solve this constrained utility maximisation problem based on a successive approximation algorithm, and conduct numerical experiments to analyse the impacts of the inventory constraint on a dealer’s terminal profit and stock inventory level. It is found that the stock inventory constraint significantly affects the terminal stock inventory level.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.230515.160316a}, url = {http://global-sci.org/intro/article_detail/eajam/10792.html} }
TY - JOUR T1 - Optimal Strategy for Limit Order Book Submissions in High Frequency Trading JO - East Asian Journal on Applied Mathematics VL - 2 SP - 222 EP - 234 PY - 2018 DA - 2018/02 SN - 6 DO - http://doi.org/10.4208/eajam.230515.160316a UR - https://global-sci.org/intro/article_detail/eajam/10792.html KW - High-frequency trading, Limit Order Book (LOB), Diffusion Approximation, Hamilton-Jacobi-Bellman (HJB) Equation. AB -

An optimal selection problem for bid and ask quotes subject to a stock inventory constraint is investigated, formulated as a constrained utility maximisation problem over a finite time horizon. The arrivals of buy and sell orders are governed by Poisson processes, and a diffusion approximation is employed on assuming the Poisson arrivals intensity is sufficiently large. Using the dynamic programming principle, we adopt an efficient numerical procedure to solve this constrained utility maximisation problem based on a successive approximation algorithm, and conduct numerical experiments to analyse the impacts of the inventory constraint on a dealer’s terminal profit and stock inventory level. It is found that the stock inventory constraint significantly affects the terminal stock inventory level.

Na Song, Yue Xie, Wai-Ki Ching, Tak-Kuen Siu & Cedric Ka-Fai Yiu. (2020). Optimal Strategy for Limit Order Book Submissions in High Frequency Trading. East Asian Journal on Applied Mathematics. 6 (2). 222-234. doi:10.4208/eajam.230515.160316a
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