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<p>This paper investigates a dynamic mean variance investment decision problem with partial information, where the stock return is assumed to consist of an observable factor and an unobservable factor, which both follow mean reversion processes. Through the Bayesian learning mechanism, the unobservable components of stock returns can be learned by investors from available information, including stock prices and observable returns. Due to lack of time consistency in dynamic investment decision problem with mean-variance criterion, the authors solve this problem by using a game theory approach and characterize the equilibrium investment strategy through the extended Hamilton-Jacobi-Bellman equation (HJB) equations system. By solving the extended HJB equations system, the semi-analytical solutions of the equilibrium strategy and the corresponding value function are obtained. In addition, the influence of unobserved predictor and learning mechanism on the equilibrium investment strategy is also analyzed by utilizing numerical examples.</p>

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Equilibrium Investment Strategy with Learning About Equity Return

  • 期刊论文

  • 发表日期：

    2025年6月9日

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  • Yongwu Li,
  • Wenchang Huang,
  • Jian Li,
  • Haixiang Yao

摘要

This paper investigates a dynamic mean variance investment decision problem with partial information, where the stock return is assumed to consist of an observable factor and an unobservable factor, which both follow mean reversion processes. Through the Bayesian learning mechanism, the unobservable components of stock returns can be learned by investors from available information, including stock prices and observable returns. Due to lack of time consistency in dynamic investment decision problem with mean-variance criterion, the authors solve this problem by using a game theory approach and characterize the equilibrium investment strategy through the extended Hamilton-Jacobi-Bellman equation (HJB) equations system. By solving the extended HJB equations system, the semi-analytical solutions of the equilibrium strategy and the corresponding value function are obtained. In addition, the influence of unobserved predictor and learning mechanism on the equilibrium investment strategy is also analyzed by utilizing numerical examples.