American Institute of Mathematical Sciences

Advanced
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
[1]

Ka Wo Lau, Yue Kuen Kwok. Optimal execution strategy of liquidation. Journal of Industrial & Management Optimization, 2006, 2 (2) : 135-144. doi: 10.3934/jimo.2006.2.135
[2]

Yong Ma, Shiping Shan, Weidong Xu. Optimal investment and consumption in the market with jump risk and capital gains tax. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1937-1953. doi: 10.3934/jimo.2018130
[3]

Chao Deng, Haixiang Yao, Yan Chen. Optimal investment and risk control problems with delay for an insurer in defaultable market. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-17. doi: 10.3934/jimo.2019070
[4]

Marcelo J. Villena, Mauricio Contreras. Global and local advertising strategies: A dynamic multi-market optimal control model. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1017-1048. doi: 10.3934/jimo.2018084
[5]

Haibo Jin, Long Hai, Xiaoliang Tang. An optimal maintenance strategy for multi-state systems based on a system linear integral equation and dynamic programming. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-26. doi: 10.3934/jimo.2018188
[6]

Jin Ma, Xinyang Wang, Jianfeng Zhang. Dynamic equilibrium limit order book model and optimal execution problem. Mathematical Control & Related Fields, 2015, 5 (3) : 557-583. doi: 10.3934/mcrf.2015.5.557
[7]

Lin Xu, Rongming Wang, Dingjun Yao. Optimal stochastic investment games under Markov regime switching market. Journal of Industrial & Management Optimization, 2014, 10 (3) : 795-815. doi: 10.3934/jimo.2014.10.795
[8]

Lisa C Flatley, Robert S MacKay, Michael Waterson. Optimal strategies for operating energy storage in an arbitrage or smoothing market. Journal of Dynamics & Games, 2016, 3 (4) : 371-398. doi: 10.3934/jdg.2016020
[9]

Po-Chung Yang, Hui-Ming Wee, Shen-Lian Chung, Yong-Yan Huang. Pricing and replenishment strategy for a multi-market deteriorating product with time-varying and price-sensitive demand. Journal of Industrial & Management Optimization, 2013, 9 (4) : 769-787. doi: 10.3934/jimo.2013.9.769
[10]

W.C. Ip, H. Wong, Jiazhu Pan, Keke Yuan. Estimating value-at-risk for chinese stock market by switching regime ARCH model. Journal of Industrial & Management Optimization, 2006, 2 (2) : 145-163. doi: 10.3934/jimo.2006.2.145
[11]

Han Yang, Jia Yue, Nan-jing Huang. Multi-objective robust cross-market mixed portfolio optimization under hierarchical risk integration. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-17. doi: 10.3934/jimo.2018177
[12]

E. Camouzis, H. Kollias, I. Leventides. Stable manifold market sequences. Journal of Dynamics & Games, 2018, 5 (2) : 165-185. doi: 10.3934/jdg.2018010
[13]

Jose S. Cánovas, María Muñoz-Guillermo. On the dynamics of a durable commodity market. Discrete & Continuous Dynamical Systems - B, 2019, 24 (12) : 6621-6631. doi: 10.3934/dcdsb.2019159
[14]

Hongming Yang, C. Y. Chung, Xiaojiao Tong, Pingping Bing. Research on dynamic equilibrium of power market with complex network constraints based on nonlinear complementarity function. Journal of Industrial & Management Optimization, 2008, 4 (3) : 617-630. doi: 10.3934/jimo.2008.4.617
[15]

Rein Luus. Optimal control of oscillatory systems by iterative dynamic programming. Journal of Industrial & Management Optimization, 2008, 4 (1) : 1-15. doi: 10.3934/jimo.2008.4.1
[16]

Lin Xu, Dingjun Yao, Gongpin Cheng. Optimal investment and dividend for an insurer under a Markov regime switching market with high gain tax. Journal of Industrial & Management Optimization, 2020, 16 (1) : 325-356. doi: 10.3934/jimo.2018154
[17]

Simone Farinelli. Geometric arbitrage theory and market dynamics. Journal of Geometric Mechanics, 2015, 7 (4) : 431-471. doi: 10.3934/jgm.2015.7.431
[18]

Alberto A. Pinto, João P. Almeida, Telmo Parreira. Local market structure in a Hotelling town. Journal of Dynamics & Games, 2016, 3 (1) : 75-100. doi: 10.3934/jdg.2016004
[19]

Lixin Wu, Fan Zhang. LIBOR market model with stochastic volatility. Journal of Industrial & Management Optimization, 2006, 2 (2) : 199-227. doi: 10.3934/jimo.2006.2.199
[20]

Didier Aussel, Rafael Correa, Matthieu Marechal. Electricity spot market with transmission losses. Journal of Industrial & Management Optimization, 2013, 9 (2) : 275-290. doi: 10.3934/jimo.2013.9.275

2018 Impact Factor: 1.025

Tools

Metrics

  • PDF downloads (15)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences