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Optimal Strategy for Limit Order Book Submissions in High Frequency Trading

Part of: Game theory Computer system organization Special processes

Published online by Cambridge University Press:  12 May 2016

Na Song ,
Yue Xie ,
Wai-Ki Ching ,
Tak-Kuen Siu  and
Cedric Ka-Fai Yiu
Na Song*
Affiliation:
School of Management and Economics, University of Electronic Science and Technology, Chengdu, China
Yue Xie*
Affiliation:
Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
Wai-Ki Ching*
Affiliation:
Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
Tak-Kuen Siu*
Affiliation:
Department of Applied Finance and Actuarial Studies, Macquarie University, Macquarie University, Sydney, NSW 2109, Australia
Cedric Ka-Fai Yiu*
Affiliation:
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
*
*Corresponding author. Email addresses:[email protected] (N. Song), [email protected] (Y. Xie), [email protected] (W.-K. Ching), [email protected] (T.-K. Siu), [email protected] (C. K.-F. Yiu)
*Corresponding author. Email addresses:[email protected] (N. Song), [email protected] (Y. Xie), [email protected] (W.-K. Ching), [email protected] (T.-K. Siu), [email protected] (C. K.-F. Yiu)
*Corresponding author. Email addresses:[email protected] (N. Song), [email protected] (Y. Xie), [email protected] (W.-K. Ching), [email protected] (T.-K. Siu), [email protected] (C. K.-F. Yiu)
*Corresponding author. Email addresses:[email protected] (N. Song), [email protected] (Y. Xie), [email protected] (W.-K. Ching), [email protected] (T.-K. Siu), [email protected] (C. K.-F. Yiu)
*Corresponding author. Email addresses:[email protected] (N. Song), [email protected] (Y. Xie), [email protected] (W.-K. Ching), [email protected] (T.-K. Siu), [email protected] (C. K.-F. Yiu)
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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.

Keywords

High-frequency tradingLimit Order Book (LOB)Diffusion ApproximationHamilton-Jacobi-Bellman (HJB) Equation

MSC classification

Secondary: 60K25: Queueing theory 68M20: Performance evaluation; queueing; scheduling 91A80: Applications of game theory
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 6 , Issue 2 , May 2016 , pp. 222 - 234
Copyright
Copyright © Global-Science Press 2016 

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