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Are Shortfall Systemic Risk Measures One Dimensional?

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  • Alessandro Doldi
  • Marco Frittelli
  • Emanuela Rosazza Gianin

Abstract

Shortfall systemic (multivariate) risk measures $\rho$ 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 $\rho$, such as dual representations, law invariance and stability.

Suggested Citation

  • Alessandro Doldi & Marco Frittelli & Emanuela Rosazza Gianin, 2023. "Are Shortfall Systemic Risk Measures One Dimensional?," Papers 2306.10752, arXiv.org.
    • Handle: RePEc:arx:papers:2306.10752
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    References listed on IDEAS

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    1. Yannick Armenti & Stéphane Crépey & Samuel Drapeau & Antonis Papapantoleon, 2018. "Multivariate Shortfall Risk Allocation and Systemic Risk," Working Papers hal-01764398, HAL.
    2. Alessandro Doldi & Marco Frittelli, 2020. "Conditional Systemic Risk Measures," Papers 2010.11515, arXiv.org, revised May 2021.
    3. Francesca Biagini & Jean-Pierre Fouque & Marco Frittelli & Thilo Meyer-Brandis, 2020. "On fairness of systemic risk measures," Finance and Stochastics, Springer, vol. 24(2), pages 513-564, April.
    4. Francesca Biagini & Jean‐Pierre Fouque & Marco Frittelli & Thilo Meyer‐Brandis, 2019. "A unified approach to systemic risk measures via acceptance sets," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 329-367, January.
    5. Marco Frittelli & Giacomo Scandolo, 2006. "Risk Measures And Capital Requirements For Processes," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 589-612, October.
    6. Ludger Overbeck & Florian Schindler, 2021. "Scalar systemic risk measures and Aumann-Shapley allocations," Papers 2112.06534, arXiv.org, revised Jul 2022.
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