# 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.

## 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.

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Item Type: Journal Article, refereed, original work 03 Faculty of Economics > Department of Banking and Finance 330 Economics Physical Sciences > Statistics and Probability Physical Sciences > Modeling and Simulation Social Sciences & Humanities > Statistics, Probability and Uncertainty English 6 September 2014 20 Feb 2015 09:28 25 Mar 2020 23:14 De Gruyter 2193-1402 Green https://doi.org/10.1515/strm-2014-0002 merlin-id:10222 : FunderSNSF: Grant ID51NF40-144611: Project TitleCapital adequacy, valuation, and portfolio selection for insurance companies

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