Robust risk measures: an averaging approach

2026-03-25

AI Summary

This work addresses the excessive conservatism of traditional worst-case risk measures under distributional uncertainty. The authors propose a weighted-average robust risk measurement framework that assigns higher weights to distributions closer to a reference model within an ambiguity set, replacing the worst-case evaluation with a weighted average of the underlying risk measure. Leveraging Banach lattice theory and Gelfand integration, they construct a convex risk measure exhibiting continuity and stability even for large ambiguity radii, and derive its dual representation. By integrating inf-convolution and quantile aggregation techniques, they establish the continuity, stability, and dominance properties of the proposed risk measure with respect to the ambiguity radius. Numerical experiments demonstrate the method’s superior calibration capability and sensitivity compared to conventional approaches.

Technology Category

• Reasoning under Uncertainty: Decision/Utility Theory
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Web measurements
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

We develop an averaging approach to robust risk measurement under payoff uncertainty. Instead of taking a worst-case value over an uncertainty neighborhood, we weight nearby payoffs more heavily under a chosen metric and average the baseline risk measure. We prove continuity in the neighborhood radius and provide a stable large-radius behavior. In Banach lattices, the approach leads to a convex risk measure and under separability of the space, a dual representation through a penalty term based on an inf-convolution taken over a Gelfand integral constraint. We also relate our veraging to aggregation at the distribution and quantile levels of payoffs, obtaining dominance and coincidence results. Numerical illustrations are conducted to verify calibration and sensitivity.

Problem

• robust risk measures
• payoff uncertainty
• averaging approach
• risk measurement
• uncertainty neighborhood

Innovation

• averaging approach
• robust risk measures
• Banach lattices
• dual representation
• inf-convolution