Robust Wasserstein Optimization and its Application in Mean-CVaR

TL;DR

This paper develops a Wasserstein-based distributionally robust optimization framework, transforming it into a penalized non-robust problem, and applies it to mean-CVaR portfolio optimization with promising empirical results.

Contribution

It introduces a novel Wasserstein ambiguity set approach and applies it to robust mean-CVaR optimization, providing a practical methodology with data-driven ambiguity set sizing.

Findings

Impressive results in US stock market experiments

Effective transformation into non-robust optimization with penalty

Demonstrates robustness against distributional uncertainty

Abstract

We refer to recent inference methodology and formulate a framework for solving the distributionally robust optimization problem, where the true probability measure is inside a Wasserstein ball around the empirical measure and the radius of the Wasserstein ball is determined by the empirical data. We transform the robust optimization into a non-robust optimization with a penalty term and provide the selection of the Wasserstein ambiguity set's size. Moreover, we apply this framework to the robust mean-CVaR optimization problem and the numerical experiments of the US stock market show impressive results compared to other popular strategies.