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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)222-234
Number of pages13
JournalEast Asian Journal on Applied Mathematics
Issue number2
Publication statusPublished - 1 May 2016


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