Abstract We characterize when a convex risk measure associated to a law-invariant acceptance set in L ∞ can be extended to L p , $1\le p<\infty $ , preserving finiteness and continuity . This problem is strongly connected to the statistical robustness of the corresponding risk measures....

Any solvency regime for financial institutions should be aligned with the two fundamental objectives of regulation: protecting liability holders and securing the stability of the financial system. From these objectives we derive two normative requirements for capital adequacy tests, called...

The theory of acceptance sets and their associated risk measures plays a key role in the design of capital adequacy tests. The objective of this paper is to investigate the class of surplus-invariant acceptance sets. We argue that surplus invariance is a reasonable requirement from a regulatory...

The theory of acceptance sets and their associated risk measures plays a key role in the design of capital adequacy tests. The objective of this paper is to investigate, in the context of bounded financial positions, the class of surplus-invariant acceptance sets. These are characterized by the...

We characterize when a convex risk measure associated to a law-invariant acceptance set in $L^\infty$ can be extended to $L^p$, $1\leq p\infty$, preserving finiteness and continuity. This problem is strongly connected to the statistical robustness of the corresponding risk measures. Special...