Optimal submission problem in a limit order book with var constraints

Na Song; Wai Ki Ching; Tak Kuen Siu; Cedric Yiu

doi:10.1109/CSO.2012.66

Optimal submission problem in a limit order book with var constraints

Na Song^*, Wai Ki Ching, Tak Kuen Siu, Cedric Yiu

^*Corresponding author for this work

Department of Applied Finance

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

2 Citations (Scopus)

Abstract

We consider an optimal selection problem for bid and ask quotes subject to a value-at-Risk (VaR) constraint when arrivals of the buy and sell orders are governed by a Poisson process. The problem is formulated as a constrained utility maximization problem over a finite time horizon. Using a diffusion approximation to Poisson arrivals of market orders, the dynamic programming principle can be applied here. We propose an efficient procedure to solve this constrained utility maximization problem based on a successive approximation algorithm. Numerical examples with and without the VaR constraint are used to illustrate the effect of the risk constraint on the dealer's choices. We also conduct numerical experiments to analyze the impacts of the risk constraint on dealer's terminal profit.

Original language	English
Title of host publication	Proceedings of the 2012 5th International Joint Conference on Computational Sciences and Optimization, CSO 2012
Editors	Lean Yu, Yuxin Zhao, Yanling Hao, Shouyang Wang
Place of Publication	Piscataway, NJ
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	266-270
Number of pages	5
ISBN (Print)	9780769546902
DOIs	https://doi.org/10.1109/CSO.2012.66
Publication status	Published - 2012
Event	2012 5th International Joint Conference on Computational Sciences and Optimization, CSO 2012 - Harbin, Heilongjiang, China Duration: 23 Jun 2012 → 26 Jun 2012

Other

Other	2012 5th International Joint Conference on Computational Sciences and Optimization, CSO 2012
Country/Territory	China
City	Harbin, Heilongjiang
Period	23/06/12 → 26/06/12

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10.1109/CSO.2012.66

Cite this

Song, N., Ching, W. K., Siu, T. K., & Yiu, C. (2012). Optimal submission problem in a limit order book with var constraints. In L. Yu, Y. Zhao, Y. Hao, & S. Wang (Eds.), Proceedings of the 2012 5th International Joint Conference on Computational Sciences and Optimization, CSO 2012 (pp. 266-270). Article 6274724 Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.1109/CSO.2012.66

Song, Na ; Ching, Wai Ki ; Siu, Tak Kuen et al. / Optimal submission problem in a limit order book with var constraints. Proceedings of the 2012 5th International Joint Conference on Computational Sciences and Optimization, CSO 2012. editor / Lean Yu ; Yuxin Zhao ; Yanling Hao ; Shouyang Wang. Piscataway, NJ : Institute of Electrical and Electronics Engineers (IEEE), 2012. pp. 266-270

@inproceedings{10277e23625844138ea6f7c72466653e,

title = "Optimal submission problem in a limit order book with var constraints",

abstract = "We consider an optimal selection problem for bid and ask quotes subject to a value-at-Risk (VaR) constraint when arrivals of the buy and sell orders are governed by a Poisson process. The problem is formulated as a constrained utility maximization problem over a finite time horizon. Using a diffusion approximation to Poisson arrivals of market orders, the dynamic programming principle can be applied here. We propose an efficient procedure to solve this constrained utility maximization problem based on a successive approximation algorithm. Numerical examples with and without the VaR constraint are used to illustrate the effect of the risk constraint on the dealer's choices. We also conduct numerical experiments to analyze the impacts of the risk constraint on dealer's terminal profit.",

author = "Na Song and Ching, {Wai Ki} and Siu, {Tak Kuen} and Cedric Yiu",

year = "2012",

doi = "10.1109/CSO.2012.66",

language = "English",

isbn = "9780769546902",

pages = "266--270",

editor = "Lean Yu and Yuxin Zhao and Yanling Hao and Shouyang Wang",

booktitle = "Proceedings of the 2012 5th International Joint Conference on Computational Sciences and Optimization, CSO 2012",

publisher = "Institute of Electrical and Electronics Engineers (IEEE)",

address = "United States",

note = "2012 5th International Joint Conference on Computational Sciences and Optimization, CSO 2012 ; Conference date: 23-06-2012 Through 26-06-2012",

}

Song, N, Ching, WK, Siu, TK & Yiu, C 2012, Optimal submission problem in a limit order book with var constraints. in L Yu, Y Zhao, Y Hao & S Wang (eds), Proceedings of the 2012 5th International Joint Conference on Computational Sciences and Optimization, CSO 2012., 6274724, Institute of Electrical and Electronics Engineers (IEEE), Piscataway, NJ, pp. 266-270, 2012 5th International Joint Conference on Computational Sciences and Optimization, CSO 2012, Harbin, Heilongjiang, China, 23/06/12. https://doi.org/10.1109/CSO.2012.66

Optimal submission problem in a limit order book with var constraints. / Song, Na; Ching, Wai Ki; Siu, Tak Kuen et al.
Proceedings of the 2012 5th International Joint Conference on Computational Sciences and Optimization, CSO 2012. ed. / Lean Yu; Yuxin Zhao; Yanling Hao; Shouyang Wang. Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE), 2012. p. 266-270 6274724.

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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AU - Siu, Tak Kuen

AU - Yiu, Cedric

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N2 - We consider an optimal selection problem for bid and ask quotes subject to a value-at-Risk (VaR) constraint when arrivals of the buy and sell orders are governed by a Poisson process. The problem is formulated as a constrained utility maximization problem over a finite time horizon. Using a diffusion approximation to Poisson arrivals of market orders, the dynamic programming principle can be applied here. We propose an efficient procedure to solve this constrained utility maximization problem based on a successive approximation algorithm. Numerical examples with and without the VaR constraint are used to illustrate the effect of the risk constraint on the dealer's choices. We also conduct numerical experiments to analyze the impacts of the risk constraint on dealer's terminal profit.

AB - We consider an optimal selection problem for bid and ask quotes subject to a value-at-Risk (VaR) constraint when arrivals of the buy and sell orders are governed by a Poisson process. The problem is formulated as a constrained utility maximization problem over a finite time horizon. Using a diffusion approximation to Poisson arrivals of market orders, the dynamic programming principle can be applied here. We propose an efficient procedure to solve this constrained utility maximization problem based on a successive approximation algorithm. Numerical examples with and without the VaR constraint are used to illustrate the effect of the risk constraint on the dealer's choices. We also conduct numerical experiments to analyze the impacts of the risk constraint on dealer's terminal profit.

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BT - Proceedings of the 2012 5th International Joint Conference on Computational Sciences and Optimization, CSO 2012

A2 - Yu, Lean

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PB - Institute of Electrical and Electronics Engineers (IEEE)

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Song N, Ching WK, Siu TK, Yiu C. Optimal submission problem in a limit order book with var constraints. In Yu L, Zhao Y, Hao Y, Wang S, editors, Proceedings of the 2012 5th International Joint Conference on Computational Sciences and Optimization, CSO 2012. Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE). 2012. p. 266-270. 6274724 doi: 10.1109/CSO.2012.66

Optimal submission problem in a limit order book with var constraints

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