On Design of Representative Distributionally Robust Formulations for Evaluation of Tail Risk Measures

2025-06-19

AI Summary

In few-shot settings, tail risk measures—such as Conditional Value-at-Risk (CVaR)—are severely biased due to data sparsity in distributional tails. To address this, this paper introduces the first systematic integration of Extreme Value Theory (EVT) into Distributionally Robust Optimization (DRO), yielding a theoretically grounded Tail-DRO framework. Our method parametrically models the tail via the Generalized Pareto Distribution (GPD), constructing an uncertainty set that balances representativeness and conservatism; it requires only scalar parameter calibration and naturally extends to multivariate settings and diverse tail-risk metrics. We establish theoretical guarantees on feasibility under limited samples. Empirical evaluation on synthetic and real-world financial/insurance datasets demonstrates that our approach yields significantly more robust and unbiased worst-case CVaR estimates compared to conventional DRO baselines, achieving consistent performance gains across all benchmarks.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Security and Privacy: Large-scale security measurements

Abstract

Conditional Value-at-Risk (CVaR) is a risk measure widely used to quantify the impact of extreme losses. Owing to the lack of representative samples CVaR is sensitive to the tails of the underlying distribution. In order to combat this sensitivity, Distributionally Robust Optimization (DRO), which evaluates the worst-case CVaR measure over a set of plausible data distributions is often deployed. Unfortunately, an improper choice of the DRO formulation can lead to a severe underestimation of tail risk. This paper aims at leveraging extreme value theory to arrive at a DRO formulation which leads to representative worst-case CVaR evaluations in that the above pitfall is avoided while simultaneously, the worst case evaluation is not a gross over-estimate of the true CVaR. We demonstrate theoretically that even when there is paucity of samples in the tail of the distribution, our formulation is readily implementable from data, only requiring calibration of a single scalar parameter. We showcase that our formulation can be easily extended to provide robustness to tail risk in multivariate applications as well as in the evaluation of other commonly used risk measures. Numerical illustrations on synthetic and real-world data showcase the practical utility of our approach.

Problem

• Design DRO formulation for accurate CVaR tail risk evaluation
• Avoid underestimation and overestimation of worst-case CVaR
• Extend robust tail risk evaluation to multivariate applications

Innovation

• Uses extreme value theory for robust CVaR
• Calibrates single scalar parameter from data
• Extends to multivariate and other risk measures