American Institute of Mathematical Sciences

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July  2005, 1(3): 289-304. doi: 10.3934/jimo.2005.1.289

Optimal execution strategy with an endogenously determined sales period

Guibin Lu 1, , Qiying Hu 2, , Youying Zhou 3, and  Wuyi Yue 4,

1. 

School of Economics and Management, Xidian University, Xi'an 710071, China
2. 

College of International Business and Management, Shanghai University, Shanghai 201800
3. 

School of Science, China iliang Uiversity, Hangzhou 310028, China
4. 

Department of Intelligence and Informatics, Konan University, 8-9-1 Okamoto, Kobe 658-8501

Received  August 2004 Revised  February 2005 Published  July 2005

We discuss the problem of the optimal liquidation of a financial product in which both the market risk of the asset and the market impact of the investor's own dealings are considered, and where the asset is liquidated over several sales periods with a constant sales interval. The investor chooses the sales volume in each period as well as the volume over the entire sales period in order to minimize the expected execution costs under a certain level of risk. We obtain an explicit solution for the optimal execution strategies and present four numerical examples to show that the proportion between market risk and liquidity risk exerts a major influence over the optimal execution strategy. We also show that to obtain the optimal result the investor should liquidate his holdings over a short sales period.
Keywords: optimal execution strategy, market impact, dynamic programming., sales period, market risk.
Mathematics Subject Classification: 37C4.
Citation: Guibin Lu, Qiying Hu, Youying Zhou, Wuyi Yue. Optimal execution strategy with an endogenously determined sales period. Journal of Industrial & Management Optimization, 2005, 1 (3) : 289-304. doi: 10.3934/jimo.2005.1.289
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