Concentration bounds for empirical conditional value-at-risk: The unbounded case
This work addresses risk assessment in decision-making under uncertainty for applications requiring control over extreme losses, though it appears incremental as it extends concentration bounds to unbounded variables.
The authors tackled the problem of estimating Conditional Value-at-Risk (CVaR) from i.i.d. samples of unbounded random variables, deriving a novel one-sided concentration bound for a sample-based estimator in sub-Gaussian or sub-exponential cases.
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.