Robust Distortion Risk Measures

43 Pages Posted: 23 Oct 2020

See all articles by Carole Bernard

Carole Bernard

Grenoble Ecole de Management; Vrije Universiteit Brussel (VUB)

Silvana M. Pesenti

University of Toronto

Steven Vanduffel

Vrije Universiteit Brussel (VUB)

Date Written: August 18, 2020


Robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance when making well-informed risk management decisions. In this paper, we quantify for any given distortion risk measure its robustness to distributional uncertainty by deriving its range of attainable values when the underlying loss distribution has a known mean and variance and furthermore lies within a ball - specified through the Wasserstein distance - around a reference distribution. We extend our results to account for uncertainty in the first two moments and provide an application to model risk assessment.

Keywords: Risk Bounds, Distortion Risk Measures, Wasserstein Distance, Distributional Robustness, Tail Value-at-Risk

JEL Classification: C52, C44, C58, G22, G23, G32

Suggested Citation

Bernard, Carole and Pesenti, Silvana M. and Vanduffel, Steven, Robust Distortion Risk Measures (August 18, 2020). Available at SSRN: or

Carole Bernard

Grenoble Ecole de Management ( email )

12, rue Pierre Sémard
Grenoble Cedex, 38003

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, 1050

Silvana M. Pesenti (Contact Author)

University of Toronto ( email )

100 St. George Street
Toronto, Ontario M5S 3G8

Steven Vanduffel

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, Brabant 1050


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