Learning Equilibrium Mean-variance Strategy

Min Dai, Yuchao Dong, Yanwei Jia

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)

Abstract

We study a dynamic mean-variance portfolio optimization problem under the reinforcement learning framework, where an entropy regularizer is introduced to induce exploration. Due to the time–inconsistency involved in a mean-variance criterion, we aim to learn an equilibrium policy. Under an incomplete market setting, we obtain a semi-analytical, exploratory, equilibrium mean-variance policy that turns out to follow a Gaussian distribution. We then focus on a Gaussian mean return model and propose a reinforcement learning algorithm to find the equilibrium policy. Thanks to a thoroughly designed policy iteration procedure in our algorithm, we prove the convergence of our algorithm under mild conditions, despite that dynamic programming principle and the usual policy improvement theorem failing to hold for an equilibrium policy. Numerical experiments are given to demonstrate our algorithm. The design and implementation of our reinforcement learning algorithm apply to a general market setup.

Original languageEnglish
Number of pages47
JournalMathematical Finance
Early online date4 Jun 2023
DOIs
Publication statusE-pub ahead of print - 4 Jun 2023

Keywords

  • asset allocation
  • entropy regularized exploration-exploitation
  • equilibrium mean variance analysis
  • reinforcement learning

ASJC Scopus subject areas

  • Accounting
  • Finance
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Applied Mathematics

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