Paper: arXiv 2405.00357

Authors: Daniel Bartl, Stephan Eckstein

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.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical and statistical foundation for a novel, adversarially robust nonparametric expected shortfall estimator. While the mathematical rigor and novelty are high, the empirical validation relies primarily on synthetic numerical experiments rather than extensive real-world market backtests.

Research Flowchart

  flowchart TD
    A[Goal: Robust & Optimal Nonparametric Estimation of Expected Shortfall] --> B[Input: Finite i.i.d. Financial Loss Data\nIncluding Heavy-Tailed & Contaminated Data]
    B --> C[Problem: Classical Plug-in Estimator Fails\nPoor Statistical Performance & Lacks Robustness]
    C --> D[Methodology: Develop Novel Estimator\nUnder Minimal Assumptions & Adversarial Setup]
    D --> E[Computation: Run Numerical Experiments\nAcross Standard Loss Distributions]
    E --> F[Outcomes: Achieves CLT-Optimal Finite-Sample Properties\n& Outperforms Plug-in Estimator]