A Computable Stochastic Riccati Equations Framework for Mean--Variance Portfolio Selection with Multifactor Stochastic Volatility Model

Abstract

We investigate a computable and empirically implementable framework for continuous-time mean--variance optimal portfolio selection with random market coefficients. The market model is built on a tractable multifactor stochastic volatility structure, which captures state-dependent risk premia, stochastic volatility, and dynamic cross-asset dependence. The optimal control is characterized by stochastic Riccati equations. On the computational side, we design an iterative BSDE-based procedure to approximate the stochastic Riccati equation from above and below, where the initial upper and lower bounds are obtained by solving two linear BSDEs. We then apply a logarithmic transformation to remove the singularity in the SRE, and solve the resulting transformed equation using both Deep BSDE and DBDP methods. The linear BSDE bounds also provide effective initial-value estimates, improving the convergence speed and training stability of the Deep BSDE solver. Empirical experiments based on sector ETF data show that the proposed multifactor mean--variance strategy produces smooth target-return wealth dynamics, with improved drawdown control and downside-risk protection relative to benchmark strategies. These results demonstrate the practical potential of combining stochastic Riccati equations, neural BSDE solvers, and multifactor market modeling for dynamic asset allocation.