On Design of Representative Distributionally Robust Formulations for Evaluation of Tail Risk Measures

• URL: http://arxiv.org/abs/2506.16230v1
• Date: Thu, 19 Jun 2025 11:40:02 GMT
• Title: On Design of Representative Distributionally Robust Formulations for Evaluation of Tail Risk Measures
• Authors: Anand Deo,
• Abstract summary: Conditional Value-at-Risk (CVaR) is a risk measure widely used to quantify the impact of extreme losses.<n>In order to combat this sensitivity, Distributionally Robust Optimization (DRO) evaluates the worst-case CVaR measure over a set of plausible data distributions.<n>This paper aims at leveraging extreme value theory to arrive at a DRO formulation which leads to representative worst-case CVaR evaluations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Conditional Value-at-Risk (CVaR) is a risk measure widely used to quantify the impact of extreme losses. Owing to the lack of representative samples CVaR is sensitive to the tails of the underlying distribution. In order to combat this sensitivity, Distributionally Robust Optimization (DRO), which evaluates the worst-case CVaR measure over a set of plausible data distributions is often deployed. Unfortunately, an improper choice of the DRO formulation can lead to a severe underestimation of tail risk. This paper aims at leveraging extreme value theory to arrive at a DRO formulation which leads to representative worst-case CVaR evaluations in that the above pitfall is avoided while simultaneously, the worst case evaluation is not a gross over-estimate of the true CVaR. We demonstrate theoretically that even when there is paucity of samples in the tail of the distribution, our formulation is readily implementable from data, only requiring calibration of a single scalar parameter. We showcase that our formulation can be easily extended to provide robustness to tail risk in multivariate applications as well as in the evaluation of other commonly used risk measures. Numerical illustrations on synthetic and real-world data showcase the practical utility of our approach.

Related papers

• Learning from Noisy Labels via Conditional Distributionally Robust Optimization [5.85767711644773]
  crowdsourcing has emerged as a practical solution for labeling large datasets. It presents a significant challenge in learning accurate models due to noisy labels from annotators with varying levels of expertise.
  arXiv  Detail & Related papers  (2024-11-26T05:03:26Z)
• Mitigating optimistic bias in entropic risk estimation and optimization with an application to insurance [5.407319151576265]
  The entropic risk measure is widely used to account for tail risks associated with an uncertain loss.<n>To mitigate the bias in the empirical entropic risk estimator, we propose a strongly consistent bootstrapping procedure.<n>We show that our methods suggest a higher (and more accurate) premium to homeowners.
  arXiv  Detail & Related papers  (2024-09-30T04:02:52Z)
• Risk and cross validation in ridge regression with correlated samples [72.59731158970894]
  We provide training examples for the in- and out-of-sample risks of ridge regression when the data points have arbitrary correlations.<n>We demonstrate that in this setting, the generalized cross validation estimator (GCV) fails to correctly predict the out-of-sample risk.<n>We further extend our analysis to the case where the test point has nontrivial correlations with the training set, a setting often encountered in time series forecasting.
  arXiv  Detail & Related papers  (2024-08-08T17:27:29Z)
• Geometry-Aware Instrumental Variable Regression [56.16884466478886]
  We propose a transport-based IV estimator that takes into account the geometry of the data manifold through data-derivative information. We provide a simple plug-and-play implementation of our method that performs on par with related estimators in standard settings.
  arXiv  Detail & Related papers  (2024-05-19T17:49:33Z)
• Data-Adaptive Tradeoffs among Multiple Risks in Distribution-Free Prediction [55.77015419028725]
  We develop methods that permit valid control of risk when threshold and tradeoff parameters are chosen adaptively. Our methodology supports monotone and nearly-monotone risks, but otherwise makes no distributional assumptions.
  arXiv  Detail & Related papers  (2024-03-28T17:28:06Z)
• On the Variance, Admissibility, and Stability of Empirical Risk Minimization [80.26309576810844]
  Empirical Risk Minimization (ERM) with squared loss may attain minimax suboptimal error rates. We show that under mild assumptions, the suboptimality of ERM must be due to large bias rather than variance. We also show that our estimates imply stability of ERM, complementing the main result of Caponnetto and Rakhlin (2006) for non-Donsker classes.
  arXiv  Detail & Related papers  (2023-05-29T15:25:48Z)
• Off-Policy Risk Assessment in Markov Decision Processes [15.225153671736201]
  We develop the first doubly robust (DR) estimator for the CDF of returns in Markov decision processes (MDPs) This estimator enjoys significantly less variance and, when the model is well specified, achieves the Cramer-Rao variance lower bound. We derive the first minimax lower bounds for off-policy CDF and risk estimation, which match our error bounds up to a constant factor.
  arXiv  Detail & Related papers  (2022-09-21T15:40:59Z)
• Distributionally Robust Models with Parametric Likelihood Ratios [123.05074253513935]
  Three simple ideas allow us to train models with DRO using a broader class of parametric likelihood ratios. We find that models trained with the resulting parametric adversaries are consistently more robust to subpopulation shifts when compared to other DRO approaches.
  arXiv  Detail & Related papers  (2022-04-13T12:43:12Z)
• Risk Minimization from Adaptively Collected Data: Guarantees for Supervised and Policy Learning [57.88785630755165]
  Empirical risk minimization (ERM) is the workhorse of machine learning, but its model-agnostic guarantees can fail when we use adaptively collected data. We study a generic importance sampling weighted ERM algorithm for using adaptively collected data to minimize the average of a loss function over a hypothesis class. For policy learning, we provide rate-optimal regret guarantees that close an open gap in the existing literature whenever exploration decays to zero.
  arXiv  Detail & Related papers  (2021-06-03T09:50:13Z)
• Bias-Corrected Peaks-Over-Threshold Estimation of the CVaR [2.552459629685159]
  Conditional value-at-risk (CVaR) is a useful risk measure in fields such as machine learning, finance, insurance, energy, etc. When measuring very extreme risk, the commonly used CVaR estimation method of sample averaging does not work well. To mitigate this problem, the CVaR can be estimated by extrapolating above a lower threshold than the VaR.
  arXiv  Detail & Related papers  (2021-03-08T20:29:06Z)
• Optimal Best-Arm Identification Methods for Tail-Risk Measures [9.128264779870538]
  Conditional value-at-risk (CVaR) and value-at-risk (VaR) are popular tail-risk measures in finance and insurance industries. We identify the smallest CVaR, VaR, or sum of CVaR and mean from amongst finitely that has smallest CVaR, VaR, or sum of CVaR and mean.
  arXiv  Detail & Related papers  (2020-08-17T20:23:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.