We present a novel approach to the portfolio selection problem for a multiperiod investor facing multiple risky assets, trading constraints, and return predictability. Our objective is to maximize mean-variance utility while addressing the computational challenges arising from the curse of dimensionality associated with dynamic programming in the presence of trading constraints. To overcome this, we employ model predictive control, a computationally efficient method for solving the problem. Additionally, we propose the use of a non-parametric Bayesian model, specifically the hierarchical Dirichlet process based Hidden Markov Model (HDP-HMM), to predict the multiperiod mean and covariance of returns. Then, we consider a time-varying maximum drawdown to adjust the risk aversion, which can effectively cope with the limit loss problems. Through extensive simulation studies and empirical analysis, we demonstrate that trading strategies based on our proposed method outperform existing approaches in out-of-sample performance.

我们为面临多种风险资产、交易限制和回报可预测性的多周期投资者提出了一种解决投资组合选择问题的新颖方法。我们的目标是最大化均值方差效用，同时解决在存在交易约束的情况下与动态规划相关的维数灾难所带来的计算挑战。为了克服这个问题，我们采用模型预测控制，这是一种解决问题的计算有效方法。此外，我们建议使用非参数贝叶斯模型，特别是基于分层狄利克雷过程的隐马尔可夫模型（HDP-HMM）来预测收益的多周期均值和协方差。然后，我们考虑时变最大回撤来调整风险厌恶程度，可以有效应对极限损失问题。