November  2010, 14(4): 1403-1417. doi: 10.3934/dcdsb.2010.14.1403

An optimal trading rule of a mean-reverting asset

1. 

Department of Mathematics, University of Georgia, Athens, GA 30602, United States, United States

Received  June 2009 Revised  November 2009 Published  August 2010

This work provides an optimal trading rule that allows buying, selling and short selling of an asset when its price is governed by mean-reverting model. The goal is to find the buy and sell prices such that the overall return (with slippage cost imposed) is maximized. The associated HJB equations (variational inequalities) are used to characterize the value functions. This paper shows that the solution of the original optimal stopping problem can be achieved by solving four algebraic equations. Numerical examples are given for demonstration.
Citation: Hoi Tin Kong, Qing Zhang. An optimal trading rule of a mean-reverting asset. Discrete and Continuous Dynamical Systems - B, 2010, 14 (4) : 1403-1417. doi: 10.3934/dcdsb.2010.14.1403
[1]

Yusuke Murase, Atsushi Kadoya, Nobuyuki Kenmochi. Optimal control problems for quasi-variational inequalities and its numerical approximation. Conference Publications, 2011, 2011 (Special) : 1101-1110. doi: 10.3934/proc.2011.2011.1101

[2]

Yin Li, Xuerong Mao, Yazhi Song, Jian Tao. Optimal investment and proportional reinsurance strategy under the mean-reverting Ornstein-Uhlenbeck process and net profit condition. Journal of Industrial and Management Optimization, 2022, 18 (1) : 75-93. doi: 10.3934/jimo.2020143

[3]

Lori Badea. Multigrid methods for some quasi-variational inequalities. Discrete and Continuous Dynamical Systems - S, 2013, 6 (6) : 1457-1471. doi: 10.3934/dcdss.2013.6.1457

[4]

Yusuke Murase, Risei Kano, Nobuyuki Kenmochi. Elliptic Quasi-variational inequalities and applications. Conference Publications, 2009, 2009 (Special) : 583-591. doi: 10.3934/proc.2009.2009.583

[5]

Yanqing Hu, Zaiming Liu, Jinbiao Wu. Optimal impulse control of a mean-reverting inventory with quadratic costs. Journal of Industrial and Management Optimization, 2018, 14 (4) : 1685-1700. doi: 10.3934/jimo.2018027

[6]

Pengxu Xie, Lihua Bai, Huayue Zhang. Optimal pairs trading of mean-reverting processes over multiple assets. Numerical Algebra, Control and Optimization, 2022  doi: 10.3934/naco.2022014

[7]

Yurii Nesterov, Laura Scrimali. Solving strongly monotone variational and quasi-variational inequalities. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1383-1396. doi: 10.3934/dcds.2011.31.1383

[8]

Laura Scrimali. Mixed behavior network equilibria and quasi-variational inequalities. Journal of Industrial and Management Optimization, 2009, 5 (2) : 363-379. doi: 10.3934/jimo.2009.5.363

[9]

Edward Allen. Environmental variability and mean-reverting processes. Discrete and Continuous Dynamical Systems - B, 2016, 21 (7) : 2073-2089. doi: 10.3934/dcdsb.2016037

[10]

Samir Adly, Tahar Haddad. On evolution quasi-variational inequalities and implicit state-dependent sweeping processes. Discrete and Continuous Dynamical Systems - S, 2020, 13 (6) : 1791-1801. doi: 10.3934/dcdss.2020105

[11]

Haisen Zhang. Clarke directional derivatives of regularized gap functions for nonsmooth quasi-variational inequalities. Mathematical Control and Related Fields, 2014, 4 (3) : 365-379. doi: 10.3934/mcrf.2014.4.365

[12]

Qihong Chen. Recovery of local volatility for financial assets with mean-reverting price processes. Mathematical Control and Related Fields, 2018, 8 (3&4) : 625-635. doi: 10.3934/mcrf.2018026

[13]

Weiwei Wang, Ping Chen. A mean-reverting currency model with floating interest rates in uncertain environment. Journal of Industrial and Management Optimization, 2019, 15 (4) : 1921-1936. doi: 10.3934/jimo.2018129

[14]

Miao Tian, Xiangfeng Yang, Yi Zhang. Lookback option pricing problem of mean-reverting stock model in uncertain environment. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2703-2714. doi: 10.3934/jimo.2020090

[15]

Wan-Hua He, Chufang Wu, Jia-Wen Gu, Wai-Ki Ching, Chi-Wing Wong. Pricing vulnerable options under a jump-diffusion model with fast mean-reverting stochastic volatility. Journal of Industrial and Management Optimization, 2022, 18 (3) : 2077-2094. doi: 10.3934/jimo.2021057

[16]

Nobuyuki Kenmochi. Parabolic quasi-variational diffusion problems with gradient constraints. Discrete and Continuous Dynamical Systems - S, 2013, 6 (2) : 423-438. doi: 10.3934/dcdss.2013.6.423

[17]

Masao Fukushima. A class of gap functions for quasi-variational inequality problems. Journal of Industrial and Management Optimization, 2007, 3 (2) : 165-171. doi: 10.3934/jimo.2007.3.165

[18]

Takeshi Fukao, Nobuyuki Kenmochi. Quasi-variational inequality approach to heat convection problems with temperature dependent velocity constraint. Discrete and Continuous Dynamical Systems, 2015, 35 (6) : 2523-2538. doi: 10.3934/dcds.2015.35.2523

[19]

Wenqing Bao, Xianyi Wu, Xian Zhou. Optimal stopping problems with restricted stopping times. Journal of Industrial and Management Optimization, 2017, 13 (1) : 399-411. doi: 10.3934/jimo.2016023

[20]

Jingzhen Liu, Ka Fai Cedric Yiu, Alain Bensoussan. Ergodic control for a mean reverting inventory model. Journal of Industrial and Management Optimization, 2018, 14 (3) : 857-876. doi: 10.3934/jimo.2017079

2021 Impact Factor: 1.497

Metrics

  • PDF downloads (95)
  • HTML views (0)
  • Cited by (7)

Other articles
by authors

[Back to Top]