References & Citations
Mathematics > Statistics Theory
Title: Monge-Kantorovich superquantiles and expected shortfalls with applications to multivariate risk measurements
(Submitted on 4 Jul 2023 (v1), last revised 19 Feb 2024 (this version, v2))
Abstract: We propose center-outward superquantile and expected shortfall functions, with applications to multivariate risk measurements, extending the standard notion of value at risk and conditional value at risk from the real line to $\mathbb{R}^d$. Our new concepts are built upon the recent definition of Monge-Kantorovich quantiles based on the theory of optimal transport, and they provide a natural way to characterize multivariate tail probabilities and central areas of point clouds. They preserve the univariate interpretation of a typical observation that lies beyond or ahead a quantile, but in a meaningful multivariate way. We show that they characterize random vectors and their convergence in distribution, which underlines their importance. Our new concepts are illustrated on both simulated and real datasets.
Submission history
From: Gauthier Thurin M [view email][v1] Tue, 4 Jul 2023 09:24:25 GMT (2803kb,D)
[v2] Mon, 19 Feb 2024 14:48:29 GMT (5223kb,D)
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