Robust risk measures: an averaging approach

TL;DR

This paper introduces a novel averaging method for robust risk measurement that weights payoffs based on proximity, ensuring stability and convexity, with theoretical guarantees and numerical validation.

Contribution

It proposes a new averaging approach to robust risk measures that improves stability, convexity, and dual representation, extending existing methods under payoff uncertainty.

Findings

The approach ensures continuity in the neighborhood radius.

It results in convex risk measures in Banach lattices.

Numerical illustrations confirm calibration and sensitivity.

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.