Constrained Optimal Execution in Limit Order Book Market with Power-shaped Market Depth

35 Pages Posted: 30 Mar 2021 Last revised: 4 Nov 2023

See all articles by Jianjun Gao

Jianjun Gao

Shanghai Jiao Tong University; Shanghai University of Finance and Economics

Chengneng Jin

Shanghai University of Finance and Economics - School of Information Management and Engineering

Weiping Wu

Fuzhou University - School of Economics and Management

Jiajia Yan

affiliation not provided to SSRN

Date Written: November 2, 2023

Abstract

This work studies the constrained optimal execution problem in a limit order book (LOB) market with a power-shaped market depth, which includes the classical block-shaped market depth as its special case. The price impact generated from our power-shaped market depth becomes a non-linear function, which aligns with the empirical studies. We also consider a class of state-dependent upper and lower bound constraints on the trading strategy, which includes non-short selling constraints as its special case. Due to the non-linear price impact and the strategy constraints, it is quite difficult to solve the problem ($\cP(\lambda,\rho^a)$) analytically. To overcome this difficulty, we propose an approximate method, provide the necessary conditions for optimal solutions in one-step transition optimization with arbitrary humped-shaped market depth, and claim that an upper bound can guarantee our approximate error. From some illustrative examples, we find that the execution policy would be significantly affected by the power-shaped market depth and the strategy constraint. For a special model with stochastic block-shaped market depth and infinite market resilience, we successfully derive the analytical solution for such an optimal execution problem by utilizing the state separation property induced from its structure. Finally, we adopt an analytical solution to demonstrate that the model does not admit a price magnification opportunity for the two-sided trading strategy.

Keywords: Optimal Execution, Limit Order Book, Market Depth, Constraints

Suggested Citation

Gao, Jianjun and Jin, Chengneng and Wu, Weiping and Yan, Jiajia, Constrained Optimal Execution in Limit Order Book Market with Power-shaped Market Depth (November 2, 2023). Available at SSRN: https://ssrn.com/abstract=3798235 or http://dx.doi.org/10.2139/ssrn.3798235

Jianjun Gao

Shanghai Jiao Tong University ( email )

800 Dongchuan Road
Shanghai
China
+86-18201925139 (Phone)
+86 34205004 (Fax)

Shanghai University of Finance and Economics ( email )

No. 100 Wudong Road
Shanghai, Shanghai 200433
China

Chengneng Jin

Shanghai University of Finance and Economics - School of Information Management and Engineering ( email )

No. 100 Wudong Road
Shanghai, Shanghai 200433
China

Weiping Wu (Contact Author)

Fuzhou University - School of Economics and Management ( email )

No. 2, Xueyuan Road, New District
No. 2, Xueyuan Road, New District
Fuzhou, Fujian 350108
China

Jiajia Yan

affiliation not provided to SSRN ( email )

No Address Available

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