Counterfactual Mean-variance Optimization

Abstract: 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.