Law-invariant risk measures: Extension properties and qualitative robustness

Law - invariant risk measures : extension properties and qualitative robustness

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

Comparative and qualitative robustness for law-invariant risk measures

Law invariant risk measures on L∞(Rd)

Kusuoka (2001) has obtained explicit representation theorems for comonotone risk measures and, more generally, for law invariant risk measures. These theorems pertain, like most of the previous literature, to the case of scalar-valued risks. Jouini-Meddeb-Touzi (2004) and Burgert-Rüschendorf (2006) extended the notion of risk measures to the vector-valued case. Recently Ekeland-Galichon-Henry (...

Bounds for nested law invariant coherent risk measures

With every law invariant coherent risk measure is associated its conditional analogue. In this paper we discuss lower and upper bounds for the corresponding nested (composite) formulations of law invariant coherent risk measures. In particular, we consider the Average Value-at-Risk and comonotonic risk measures. © 2012 Elsevier B.V. All rights reserved.

Law invariant convex risk measures for portfolio vectors

The class of all law invariant, convex risk measures for portfolio vectors is characterized. The building blocks of this class are shown to be formed by the maximal correlation risk measures. We introduce some classes of multivariate distortion risk measures and relate them to multivariate quantile functionals and to an extension of the average value at risk measure.