Optimal nonparametric estimation of the expected shortfall risk

TL;DR

This paper introduces a robust, nonparametric estimator for expected shortfall risk that outperforms traditional methods, especially under heavy-tailed distributions and data contamination, with proven optimal statistical properties.

Contribution

The paper proposes a novel, adversarially robust estimator for expected shortfall that achieves optimal statistical performance under minimal assumptions and withstands data manipulation.

Findings

Outperforms classical plug-in estimator in simulations

Achieves optimal statistical properties under minimal assumptions

Remains effective even with malicious data modifications

Abstract

We address the problem of estimating the expected shortfall risk of a financial loss using a finite number of i.i.d. data. It is well known that the classical plug-in estimator suffers from poor statistical performance when faced with (heavy-tailed) distributions that are commonly used in financial contexts. Further, it lacks robustness, as the modification of even a single data point can cause a significant distortion. We propose a novel procedure for the estimation of the expected shortfall and prove that it recovers the best possible statistical properties (dictated by the central limit theorem) under minimal assumptions and for all finite numbers of data. Further, this estimator is adversarially robust: even if a (small) proportion of the data is maliciously modified, the procedure continuous to optimally estimate the true expected shortfall risk. We demonstrate that our estimator outperforms the classical plug-in estimator through a variety of numerical experiments across a range of standard loss distributions.