反事实均值-方差优化
Counterfactual Mean-variance Optimization
AI总结：
本文研究反事实均值-方差优化问题，提出双重稳健风格的最优解估计量，推导其渐近分布，并通过协方差校准提升有限样本性能，应用于医疗政策与金融投资组合。
摘要：
我们研究了一种反事实均值-方差优化问题，其中均值和方差被定义为反事实分布的泛函。该优化问题在由特定干预所诱导的假设情景下，定义了各种约束条件下的最优资源配置，该情景可能与观测到的世界存在显著差异。我们为反事实均值-方差优化问题的最优解提出了一种双重稳健风格的估计量，并推导出其渐近分布的闭式表达式。我们的分析表明，所提出的估计量能够达到快速的参数收敛速度，同时即使结合非参数方法也能实现可处理的推断。我们进一步解决了反事实协方差估计量的校准问题，以增强所提出的最优解估计量的有限样本性能。最后，我们通过模拟研究评估了所提出的方法，并展示了它们在涉及医疗政策和金融投资组合构建的现实问题中的适用性。
英文摘要：
We study a counterfactual mean-variance optimization, where the mean and variance are defined as functionals of counterfactual distributions. The optimization problem defines the optimal resource allocation under various constraints in a hypothetical scenario induced by a specified intervention, which may differ substantially from the observed world. We propose a doubly robust-style estimator for the optimal solution to the counterfactual mean-variance optimization problem and derive a closed-form expression for its asymptotic distribution. Our analysis shows that the proposed estimator attains fast parametric convergence rates while enabling tractable inference, even when incorporating nonparametric methods. We further address the calibration of the counterfactual covariance estimator to enhance the finite-sample performance of the proposed optimal solution estimators. Finally, we evaluate the proposed methods through simulation studies and demonstrate their applicability in real-world problems involving healthcare policy and financial portfolio construction.
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