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On fairness of systemic risk measures

Author

Listed:
  • Francesca Biagini

    (University of Munich
    University of Oslo)

  • Jean-Pierre Fouque

    (University of California)

  • Marco Frittelli

    (Università degli Studi di Milano)

  • Thilo Meyer-Brandis

    (University of Munich)

Abstract

In our previous paper “A unified approach to systemic risk measures via acceptance sets” (Mathematical Finance, 2018), we have introduced a general class of systemic risk measures that allow random allocations to individual banks before aggregation of their risks. In the present paper, we prove a dual representation of a particular subclass of such systemic risk measures and the existence and uniqueness of the optimal allocation related to them. We also introduce an associated utility maximisation problem which has the same solution as the minimisation problem associated to the systemic risk measure. In addition, the optimiser in the dual formulation provides a risk allocation which is fair from the point of view of the individual financial institutions. The case with exponential utilities which allows explicit computation is treated in detail.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:finsto:v:24:y:2020:i:2:d:10.1007_s00780-020-00417-4
    DOI: 10.1007/s00780-020-00417-4
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    References listed on IDEAS

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    Cited by:

    1. Francesca Biagini & Alessandro Doldi & Jean-Pierre Fouque & Marco Frittelli & Thilo Meyer-Brandis, 2023. "Collective Arbitrage and the Value of Cooperation," Papers 2306.11599, arXiv.org, revised May 2024.
    2. Matteo Burzoni & Marco Frittelli & Federico Zorzi, 2021. "Robust market-adjusted systemic risk measures," Papers 2103.02920, arXiv.org, revised Aug 2021.
    3. Alessandro Doldi & Marco Frittelli, 2021. "Real-Valued Systemic Risk Measures," Mathematics, MDPI, vol. 9(9), pages 1-24, April.
    4. Ludger Overbeck & Florian Schindler, 2021. "Scalar systemic risk measures and Aumann-Shapley allocations," Papers 2112.06534, arXiv.org, revised Jul 2022.
    5. Alessandro Doldi & Marco Frittelli & Emanuela Rosazza Gianin, 2023. "Are Shortfall Systemic Risk Measures One Dimensional?," Papers 2306.10752, arXiv.org.
    6. Yichen Feng & Jean-Pierre Fouque & Ruimeng Hu & Tomoyuki Ichiba, 2022. "Systemic Risk Models for Disjoint and Overlapping Groups with Equilibrium Strategies," Papers 2202.00662, arXiv.org.
    7. Lukas Gonon & Thilo Meyer-Brandis & Niklas Weber, 2024. "Computing Systemic Risk Measures with Graph Neural Networks," Papers 2410.07222, arXiv.org.
    8. Alessandro Doldi & Marco Frittelli, 2020. "Conditional Systemic Risk Measures," Papers 2010.11515, arXiv.org, revised May 2021.

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    More about this item

    Keywords

    Systemic risk measures; Random allocations; Risk allocation; Fairness;
    All these keywords.

    JEL classification:

    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • G1 - Financial Economics - - General Financial Markets

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