# Law-invariant risk measures: Extension properties and qualitative robustness

Koch-Medina, Pablo; Munari, Cosimo (2014). Law-invariant risk measures: Extension properties and qualitative robustness. Statistics & Risk Modeling, 31(3):1-22.

## Abstract

We characterize when a convex risk measure associated to a law-invariant acceptance set in L$^∞$ can be extended to L$^p$, 1≤p<∞, preserving finiteness and continuity. This problem is strongly connected to the statistical robustness of the corresponding risk measures. Special attention is paid to concrete examples including risk measures based on expected utility, max-correlation risk measures, and distortion risk measures.

We characterize when a convex risk measure associated to a law-invariant acceptance set in L$^∞$ can be extended to L$^p$, 1≤p<∞, preserving finiteness and continuity. This problem is strongly connected to the statistical robustness of the corresponding risk measures. Special attention is paid to concrete examples including risk measures based on expected utility, max-correlation risk measures, and distortion risk measures.

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Item Type: Journal Article, refereed, original work 03 Faculty of Economics > Department of Banking and Finance 330 Economics English 6 September 2014 20 Feb 2015 09:28 05 Apr 2016 18:58 De Gruyter Oldenbourg 2196-7040 https://doi.org/10.1515/strm-2014-0002 merlin-id:10222
Permanent URL: https://doi.org/10.5167/uzh-107102