AI 中文总结
该研究提出多因子随机波动率模型下的随机Riccati方程框架，结合Deep BSDE与DBDP方法求解，所得投资策略在回撤控制等方面优于基准策略，为动态资产配置提供了可行方案。
AI 中文摘要
我们研究了带有随机市场系数的连续时间均值-方差最优投资组合选择的可计算且可实证实现的框架。该市场模型构建于易于处理的多因子随机波动率结构之上，该结构能捕捉状态依赖的风险溢价、随机波动率以及动态跨资产依赖关系。最优控制由随机Riccati方程（SRE）刻画。在计算方面，我们设计了一种基于倒向随机微分方程（BSDE）的迭代程序，用于从上下两个方向近似随机Riccati方程，其中初始上下界通过求解两个线性BSDE得到。随后，我们应用对数变换消除SRE中的奇异性，并使用Deep BSDE和DBDP方法求解变换后的方程。这些线性BSDE界还能提供有效的初值估计，提升Deep BSDE求解器的收敛速度和训练稳定性。基于行业ETF数据的实证实验表明，所提出的多因子均值-方差策略能产生平稳的目标收益财富动态，相较于基准策略，其回撤控制和下行风险保护均有所提升。这些结果证明了将随机Riccati方程、神经BSDE求解器与多因子市场建模相结合，应用于动态资产配置的实际潜力。
英文摘要
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.
