Paper: arXiv 2610.09622

Authors: Yang Liu, Qiuqi Wang, Yihan Wang

Abstract

Risk evaluation under distributional ambiguity is central to decision making in finance, economics, and operations research. Wasserstein balls provide a natural way to describe uncertainty around a reference distribution. We solve a natural yet open problem of robust optimization for the class of distortion riskmetrics with Wasserstein distance as the sole ambiguity constraint. This chosen objective class does not require convexity, monotonicity, and continuity of distortion functions, encompassing many common risk measures and deviation measures. First, we characterize conditions under which direct convexification preserves the worst-case value. Second, we develop a constructive method for exact worst-case evaluation when the direct convexification conditions fail. Third, we construct explicit approximate worst-case distributions and provide computable error bounds to assess their accuracy without solving the exact problem. We apply these results to distributionally robust portfolio selection and use numerical experiments to assess approximation accuracy and the resulting portfolio decisions.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical and theoretical approach to robust risk management, tackling a complex problem with novel solutions. While it includes numerical experiments, the core contribution is in its rigorous mathematical derivations and theoretical framework. The clarity is good given the complexity, but reproducibility is hard to assess without code.

Research Flowchart

  flowchart TD
    A[Research Goal: Robust Distortion Riskmetrics under Wasserstein Ambiguity] --> B{Key Methodology: Robust Optimization for Distortion Riskmetrics};
    B --> C{Inputs: Wasserstein Distance, Reference Distribution, Distortion Functions};
    C --> D{Computational Process 1: Characterize Direct Convexification Conditions};
    C --> E{Computational Process 2: Exact Worst-Case Evaluation (if convexification fails)};
    C --> F{Computational Process 3: Approximate Worst-Case Distributions & Error Bounds};
    D & E & F --> G[Key Findings: Conditions for Convexification, Exact & Approximate Solutions, Applications to Portfolio Selection];