Concentration bounds for empirical conditional value-at-risk: the unbounded case. (English) Zbl 1476.91220
Summary: Conditional Value-at-Risk (CVaR) is a popular risk measure for modelling losses in the case of a rare but extreme event. 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.
MSC:
| 91G70 | Statistical methods; risk measures |
Keywords:
value-at-risk; conditional value-at-risk; concentration bounds; sub-Gaussian distributions; sub-exponential distributionsReferences:
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