Law - invariant risk measures : extension properties and qualitative robustness

Comparative and qualitative robustness for law-invariant risk measures

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.

Kusuoka Representations of Coherent Risk Measures in Finite Probability Spaces

Kusuoka representations provide an important and useful characterization of law invariant coherent risk measures in atomless probability spaces. However, the applicability of these results is limited by the fact that such representations do not always exist in probability spaces with atoms, such as finite probability spaces. We introduce the class of functionally coherent risk measures, which a...

Optimal Risk Sharing for Law Invariant Monetary Utility Functions

We consider the problem of optimal risk sharing of some given total risk between two economic agents characterized by law-invariant monetary utility functions or equivalently, law-invariant risk measures. We first prove existence of an optimal risk sharing allocation which is in addition increasing in terms of the total risk. We next provide an explicit characterization in the case where both a...

Risk measures with the CxLS property

A law invariant risk measure ρ has the Convex Levels Sets property (CxLS) if ρ(F ) = ρ(G) = γ ⇒ ρ(λF + (1− λ)G) = γ, for each γ ∈ (0, 1). The level sets of ρ are convex with respect to mixtures of distributions; such a convexity has not to be confused with convexity or quasi-convexity with respect to sums of random variables. In the axiomatic theory of risk measures, the CxLS property arises na...