Paper ID: | 6260 |
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Title: | Concentration of risk measures: A Wasserstein distance approach |

The paper is concerned with deriving concentration bounds for measures of 'risk' (e.g. the risk of a portfolio) in financial applications, e.g. CVar, and generalizations thereof, some of which can roughly be viewed as expected deviations from quantiles of a distribution. The main contribution is to remark that changes in risks over two distributions can be bounded through the (l1) Wasserstein distance. Concentration bounds for Wasserstein distance can then be applied. The approach yields 2-sided concentration bounds (for empirical version of such measures) which apparently were not previously obtained, or obtained under stronger boundedness conditions. Authors also discuss achieving 'tighter' bounds than previous one-sided bounds under tail conditions (e..g Gaussian tails), but however do not provide those previous bounds for comparison in neither the main paper nor the rebuttal. In summary, the paper is interesting in deriving a different approach for obtaining concentration results for complex functionals of a distribution, but however might not necessarily be of interest to a large ML audience given the narrow focus in Finance.