# Concentration bounds for empirical conditional value-at-risk: The unbounded case

arXiv: https://arxiv.org/abs/1808.01739 · HTML: https://mlsanity.com/paper/1808.01739/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Aug 2018.

## Built on by (most cited first, 13 of 13)

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- [Conformal Predictions under Markovian Data](https://mlsanity.com/paper/2407.15277/) (2024)
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- [Distribution-Free Model-Agnostic Regression Calibration via Nonparametric Methods](https://mlsanity.com/paper/2305.12283/) (2023)
- [A Distribution Optimization Framework for Confidence Bounds of Risk Measures](https://mlsanity.com/paper/2306.07059/) (2023)
- [Risk Estimation in a Markov Cost Process: Lower and Upper Bounds](https://mlsanity.com/paper/2310.11389/) (2023)
- [Risk averse non-stationary multi-armed bandits](https://mlsanity.com/paper/2109.13977/) (2021)
- [Order Optimal Regret Bounds for Sharpe Ratio Optimization under Thompson Sampling](https://mlsanity.com/paper/2508.13749/) (2025)
- [Distorted Distributional Policy Evaluation for Offline Reinforcement Learning](https://mlsanity.com/paper/2601.01917/) (2026)

## Abstract (arXiv)

In several real-world applications involving decision making under uncertainty, the traditional expected value objective may not be suitable, as it may be necessary to control losses in the case of a rare but extreme event. Conditional Value-at-Risk (CVaR) is a popular risk measure for modeling the aforementioned objective. We consider the problem of estimating CVaR from i.i.d. samples of an unbounded random variable, which is either sub-Gaussian or sub-exponential. We derive a novel one-sided concentration bound for a natural sample-based CVaR estimator in this setting. Our bound relies on a concentration result for a quantile-based estimator for Value-at-Risk (VaR), which may be of independent interest.