EVT-Based Rate-Preserving Distributional Robustness for Tail Risk Functionals

Paper: arXiv 2506.16230

Authors: Anand Deo

Abstract

Risk measures such as Conditional Value-at-Risk (CVaR) focus on extreme losses, where scarce tail data makes model error unavoidable. To hedge misspecification, one evaluates worst-case tail risk over an ambiguity set. Using Extreme Value Theory (EVT), we derive first-order asymptotics for worst-case tail risk for a broad class of tail-risk measures under standard ambiguity sets, including Wasserstein balls and $φ$-divergence neighborhoods. We show that robustification can alter the nominal tail asymptotic scaling as the tail level $β\to0$, leading to excess risk inflation. Motivated by this diagnostic, we propose a tail-calibrated ambiguity design that preserves the nominal tail asymptotic scaling while still guarding against misspecification. Under standard domain of attraction assumptions, we prove that the resulting worst-case risk preserves the baseline first-order scaling as $β\to0$, uniformly over key tuning parameters, and that a plug-in implementation based on consistent tail-index estimation inherits these guarantees. Synthetic and real-data experiments show that the proposed design avoids the severe inflation often induced by standard ambiguity sets.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides rigorous mathematical proofs combining Extreme Value Theory (EVT) and Distributionally Robust Optimization (DRO) to address excess risk inflation in tail risk functionals. While it features solid synthetic and real-data validations (e.g., Danish fire losses, Fama-French factors), the reproducibility score is slightly constrained by the lack of direct links to open-source code repositories in the text excerpt.

Research Flowchart

  flowchart TD
    A["<b>Research Goal</b><br>Evaluate and improve worst-case tail risk (e.g., CVaR) under distributionally robust ambiguity sets"] --> B["<b>Problem Analysis & EVT Derivation</b><br>Apply Extreme Value Theory to analyze asymptotics as β → 0"]
    
    B --> C{"<b>Diagnostic Finding</b><br>Standard ambiguity sets (Wasserstein, φ-divergence) cause excess risk inflation and alter nominal tail scaling"}
    
    C --> D["<b>Proposed Solution</b><br>Design a Tail-Calibrated Ambiguity Set to preserve nominal tail asymptotic scaling"]
    
    E["<b>Inputs & Data</b><br>Tail level β, Domain of Attraction assumptions, Tail-index estimation, Synthetic & Real Cross-Asset Data"] --> F["<b>Computational Processes</b><br>Plug-in EVT estimation, baseline vs. robust tail-risk optimization, and cross-asset empirical evaluation"]
    
    D --> F
    
    F --> G["<b>Key Outcomes</b><br>Preserved baseline scaling as β → 0, uniform robustness guarantees, and avoidance of severe risk inflation"]

Cited References (291)

1. Machine learning and portfolio optimization (2018)
2. State-dependent importance sampling for rare-event simulation: An overview and recent advances. (2012)
3. Quantifying distributional model risk via optimal transport (2019)
4. Probability-1 (2016)
5. On approximations of data-driven chance constrained programs over Wasserstein balls (2023)
6. Characterizing the Minimum Cost to Achieve High Reliability via Asymptotic Analysis of Chance Constrained Programs (2024)
7. The modelling of operational risk: experience with the analysis of the data collected by the Basel Committee (2004)
8. A high quantile estimator based on the log-generalized Weibull tail limit (2018)

1 of 291 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.