Short Communication: Are Shortfall Systemic Risk Measures One Dimensional?

Abstract

Shortfall systemic (multivariate) risk measures ρ defined through an N -dimensional multivariate utility function U and random allocations can be represented as classical (one dimensional) shortfall risk measures associated to an explicitly determined 1-dimensional function constructed from U . This finding allows for simplifying the study of several properties of ρ, such as dual representations, law invariance and stability.