Concentration bounds for empirical conditional value-at-risk: The unbounded case
Machine Learning
2018-08-07 v1 Machine Learning
Abstract
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.
Cite
@article{arxiv.1808.01739,
title = {Concentration bounds for empirical conditional value-at-risk: The unbounded case},
author = {Ravi Kumar Kolla and Prashanth L. A. and Sanjay P. Bhat and Krishna Jagannathan},
journal= {arXiv preprint arXiv:1808.01739},
year = {2018}
}