What's in a ball? Constructing and characterizing uncertainty sets

TL;DR

This paper introduces a new family of divergence measures for constructing uncertainty sets in robust modeling, addressing limitations of existing measures for heavy-tailed models like lognormal distributions.

Contribution

It proposes a novel divergence measure that better captures moderate tail risks, improving robustness analysis for heavy-tailed reference models.

Findings

Existing measures are inadequate for heavy-tailed models.

The new divergence captures intermediate levels of model risk.

Improves robustness analysis for fat-tailed distributions.

Abstract

In the presence of model risk, it is well-established to replace classical expected values by worst-case expectations over all models within a fixed radius from a given reference model. This is the "robustness" approach. We show that previous methods for measuring this radius, e.g. relative entropy or polynomial divergences, are inadequate for reference models which are moderately heavy-tailed such as lognormal models. Worst cases are either infinitely pessimistic, or they rule out the possibility of fat-tailed "power law" models as plausible alternatives. We introduce a new family of divergence measures which captures intermediate levels of pessimism.