Open-loop equilibrium strategy for mean-variance portfolio selection: A log-return model

Jiannan Zhang, Ping Chen, Zhuo Jin, Shuanming Li

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


This paper investigates a continuous-time mean-variance portfolio selection problem based on a log-return model. The financial market is composed of one risk-free asset and multiple risky assets whose prices are modelled by geometric Brownian motions. We derive a sufficient condition for open-loop equilibrium strategies via forward backward stochastic differential equations (FBSDEs). An equilibrium strategy is derived by solving the system. To illustrate our result, we consider a special case where the interest rate process is described by the Vasicek model. In this case, we also derive the closed-loop equilibrium strategy through the dynamic programming approach.
Original languageEnglish
Pages (from-to)765-777
Number of pages13
JournalJournal of Industrial and Management Optimization
Issue number2
Publication statusPublished - Mar 2021
Externally publishedYes


  • Mean-variance
  • log-return
  • time-consistent
  • open-loop equilibrium strategy
  • closed-loop equilibrium strategy


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