Counterfactual Mean-variance Optimization

TL;DR

This paper introduces a novel counterfactual mean-variance optimization framework with a robust estimator, enabling effective resource allocation analysis under hypothetical interventions in finance and healthcare.

Contribution

It develops a doubly robust estimator for counterfactual mean-variance optimization and provides theoretical guarantees for its fast convergence and inference capabilities.

Findings

Estimator achieves parametric convergence rates

Method performs well in simulation studies

Applicable to healthcare policy and financial portfolios

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.