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arXiv · 1901.00997

Concentration bounds for CVaR estimation: The cases of light-tailed and heavy-tailed distributions

Prashanth L. A.·Krishna Jagannathan·Ravi Kumar Kolla
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Abstract

Conditional Value-at-Risk (CVaR) is a widely used risk metric in applications such as finance. We derive concentration bounds for CVaR estimates, considering separately the cases of light-tailed and heavy-tailed distributions. In the light-tailed case, we use a classical CVaR estimator based on the empirical distribution constructed from the samples. For heavy-tailed random variables, we assume a mild `bounded moment' condition, and derive a concentration bound for a truncation-based estimator. Notably, our concentration bounds enjoy an exponential decay in the sample size, for heavy-tailed as well as light-tailed distributions. To demonstrate the applicability of our concentration results, we consider a CVaR optimization problem in a multi-armed bandit setting. Specifically, we address the best CVaR-arm identification problem under a fixed budget. We modify the well-known successive rejects algorithm to incorporate a CVaR-based criterion. Using the CVaR concentration result, we derive an upper-bound on the probability of incorrect identification by the proposed algorithm.

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Prashanth L. A., Krishna Jagannathan, Ravi Kumar Kolla. 2019-08-25. Concentration bounds for CVaR estimation: The cases of light-tailed and heavy-tailed distributions. https://arxiv.org/abs/1901.00997

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