Are Shortfall Systemic Risk Measures One Dimensional?
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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