Are Shortfall Systemic Risk Measures One Dimensional?

Doldi Alessandro, University of Florence
Frittelli Marco, Università degli Studi di Milano
Rosazza Gianin Emanuela, University of Milano Bicocca

In this talk we show that shortfall systemic (multivariate) risk measures $\rho$ defined through an N-dimensional multivariate utility function $U$ and random allocations (see \cite{armenti}, \cite{FFFM}, \cite{DF}) can be represented as classical (one dimensional) shortfall risk measures associated to an explicitly determined 1-dimensional function constructed from $U$. The study of several properties of shortfall systemic (multivariate) risk measures $\rho$, such as law invariance and a Law of Large Numbers-type result, is then simplified by applying the findings above. Joint work with Alessandro Doldi and Marco Frittelli.

Area: CS14 - Stochastic models for risk and cooperation (Giacomo Scandolo and Alessandro Doldi)

Keywords: systemic risk measures; shortfall risk measures; dimensionality reduction

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