# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2021109
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## Generalized optimal liquidation problems across multiple trading venues

 1 Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, China 2 Department of Mathematics, Southern University of Science and Technology, Shenzhen, China 3 Department of Actuarial Studies and Business Analytics, Macquarie Business School, Macquarie University, Sydney, Australia

Received  October 2019 Revised  April 2021 Early access June 2021

In this paper, we generalize the Almgren-Chriss's market impact model to a more realistic and flexible framework and employ it to derive and analyze some aspects of optimal liquidation problem in a security market. We illustrate how a trader's liquidation strategy alters when multiple venues and extra information are brought into the security market and detected by the trader. This study gives some new insights into the relationship between liquidation strategy and market liquidity, and provides a multi-scale approach to the optimal liquidation problem with randomly varying volatility.

Citation: Qing-Qing Yang, Wai-Ki Ching, Jia-Wen Gu, Tak-Kuen Siu. Generalized optimal liquidation problems across multiple trading venues. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021109
##### References:

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##### References:
The performance of the "Constant-Vol" strategy
1, 000 simulations with $Q = 100, s = 15,$ w.r.t. $\mathcal R_T$
 Statistics Constant-Vol Vol-adjust Mean -300.70 -288.46 Std 54.76 27.45 Skewness 1.03 0.24 Kurtosis 5.26 3.05 Objective function -577.58 -560.36
 Statistics Constant-Vol Vol-adjust Mean -300.70 -288.46 Std 54.76 27.45 Skewness 1.03 0.24 Kurtosis 5.26 3.05 Objective function -577.58 -560.36
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