Shortfall systemic (multivariate) risk measures ρ defined through an N-dimensional multivariate utility function U and random allocations can be represented as classical (1-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.
Doldi, A., Frittelli, M., Rosazza Gianin, E. (2024). Short Communication: Are Shortfall Systemic Risk Measures One Dimensional?. SIAM JOURNAL ON FINANCIAL MATHEMATICS, 15(1), 1-14 [10.1137/23M1580413].
Short Communication: Are Shortfall Systemic Risk Measures One Dimensional?
Frittelli, M;Rosazza Gianin, E
2024
Abstract
Shortfall systemic (multivariate) risk measures ρ defined through an N-dimensional multivariate utility function U and random allocations can be represented as classical (1-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.
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