Optimal Pairs Trading Strategies

A Stochastic Mean–Variance Approach

Journal article (2022)

Authors

F. Yu Applied Probability - EEMCS
Wai Ki Ching Hughes Hall, The University of Hong Kong
Chufang Wu Southern University of Science and Technology, The University of Hong Kong
Jia Wen Gu Southern University of Science and Technology
Research Group
Applied Probability (EEMCS) (TU Delft)
Copyright: © 2022 F. Yu, Wai Ki Ching, Chufang Wu, Jia Wen Gu
DOI: https://doi.org/10.1007/s10957-022-02131-x
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Published Date

2022

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

Abstract

In this paper, we consider optimal pairs trading strategies in terms of static optimality and dynamic optimality under mean–variance criterion. The spread of the entity pairs is assumed to be mean-reverting and follows an Ornstein–Uhlenbeck process. A constrained optimal control problem is considered, and the Lagrange multiplier technique is adopted to transform the primal problem into a family of linear-quadratic optimal control problems that can be solved by the classical dynamic programming principle. Both solutions for static and dynamic optimal pairs trading problems are derived and discussed. We show that the “static and dynamic optimality” is a viable approach to the time-inconsistent control problem. Furthermore, numerical experiments are presented to demonstrate the performance of the optimal pairs trading strategies.

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