Robust Wasserstein Optimization and its Application in Mean-CVaR

Paper: arXiv 2306.15524

Authors: Xin Hai, Kihun Nam

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a mathematically rigorous framework applying Wasserstein distributionally robust optimization (DRO) to mean-CVaR portfolio selection, reformulating it into a tractable non-robust penalized problem. The empirical validation on US equities demonstrates practical utility, though additional backtesting detail and code availability would strengthen reproducibility.

Research Flowchart

  flowchart TD
    A[Research Goal: Robust Mean-CVaR Portfolio Optimization] --> B[Data Input: US Stock Market Empirical Returns]
    B --> C[Construct Wasserstein Ambiguity Set around Empirical Measure]
    C --> D[Transform Distributionally Robust Problem to Non-Robust Model with Penalty Term]
    D --> E[Data-Driven Calibration of Wasserstein Ball Radius]
    E --> F[Execute Portfolio Optimization & Numerical Experiments]
    F --> G[Key Outcome: Superior Out-of-Sample Performance vs. Standard Strategies]