We characterize when a convex risk measure associated to a law-invariant acceptance set of bounded random variables can be extended to a larger lebesgue space 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.
Law-invariant risk measures: Extension properties and qualitative robustness
Munari C
2014-01-01
Abstract
We characterize when a convex risk measure associated to a law-invariant acceptance set of bounded random variables can be extended to a larger lebesgue space 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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