Law-invariant risk measures: extension properties and qualitative robustness

Original · EN

We characterize when a convex risk measure associated to a law-invariant acceptance set in L∞ can be extended to Lᵖ, 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.