Pairs trading with illiquidity and position limits

Menglu FENG, Mei Choi CHIU, Hoi Ying WONG

Research output: Contribution to journalArticlespeer-review


We investigate the optimal investment among the money market account, a liquid risky asset (e.g. stock index) and an illiquid risky asset (e.g. individual stock), where the two risky assets are cointegrated. The illiquid risky asset is subject to a proportional transaction cost and the portfolio of the three assets faces certain position limits. We develop the optimal investment strategy to maximize the gain function, which is realized through an expected sum of discounted utilities given transaction costs and position limits. The problem formulation uses a singular control framework with cointegration that determines optimal trading boundaries among holding, selling and no-trading regions. We conduct comprehensive numerical analysis on the optimal investment strategy and features of the optimal trading boundaries given various levels of position limits. Copyright © 2019 American Institute of Mathematical Sciences.
Original languageEnglish
JournalJournal of Industrial and Management Optimization
Publication statusE-pub ahead of print - Jul 2019


Feng, M., Chiu, M. C., & Wong, H. Y. (2019). Pairs trading with illiquidity and position limits. Journal of Industrial and Management Optimization. Advance online publication. doi: 10.3934/jimo.2019090


  • Cointegration
  • Liquidity
  • Pairs trading
  • Position limits
  • Singular control problem

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