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An Optimal Strategy for Pairs Trading Under Geometric Brownian Motions
Tie, Jingzhi1; Zhang, Hanqin2,3; Zhang, Qing1
2018-11-01
Source PublicationJOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
ISSN0022-3239
Volume179Issue:2Pages:654-675
AbstractThis paper is concerned with an optimal strategy for simultaneously trading of a pair of stocks. The idea of pairs trading is to monitor their price movements and compare their relative strength over time. A pairs trade is triggered by their prices divergence and consists of a pair of positions to short the strong stock and to long the weak one. Such a strategy bets on the reversal of their price strengths. From the viewpoint of technical tractability, typical pairs-trading models usually assume a difference of the stock prices satisfies a mean-reversion equation. In this paper, we consider the optimal pairs-trading problem by allowing the stock prices to follow general geometric Brownian motions. The objective is to trade the pairs over time to maximize an overall return with a fixed commission cost for each transaction. The optimal policy is characterized by threshold curves obtained by solving the associated HJB equations. Numerical examples are included to demonstrate the dependence of our trading rules on various parameters and to illustrate how to implement the results in practice.
KeywordPairs trading Optimal policy Quasi-variational inequalities 93E20 91G80 49L20
DOI10.1007/s10957-017-1065-8
Language英语
Funding ProjectSimons Foundation[235179]
WOS Research AreaOperations Research & Management Science ; Mathematics
WOS SubjectOperations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000447518900012
PublisherSPRINGER/PLENUM PUBLISHERS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31356
Collection应用数学研究所
Affiliation1.Univ Georgia, Dept Math, Athens, GA 30602 USA
2.Acad Sinica, Acad Math & Syst Sci, Beijing 100190, Peoples R China
3.Natl Univ Singapore, Sch Business, Singapore 119245, Singapore
Recommended Citation
GB/T 7714
Tie, Jingzhi,Zhang, Hanqin,Zhang, Qing. An Optimal Strategy for Pairs Trading Under Geometric Brownian Motions[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS,2018,179(2):654-675.
APA Tie, Jingzhi,Zhang, Hanqin,&Zhang, Qing.(2018).An Optimal Strategy for Pairs Trading Under Geometric Brownian Motions.JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS,179(2),654-675.
MLA Tie, Jingzhi,et al."An Optimal Strategy for Pairs Trading Under Geometric Brownian Motions".JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 179.2(2018):654-675.
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