IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v24y2020i2d10.1007_s00780-020-00417-4.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00780-020-00417-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00780-020-00417-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Marco Frittelli & Giacomo Scandolo, 2006. "Risk Measures And Capital Requirements For Processes," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 589-612, October.
    2. Craig, Ben & von Peter, Goetz, 2014. "Interbank tiering and money center banks," Journal of Financial Intermediation, Elsevier, vol. 23(3), pages 322-347.
    3. Gai, Prasanna & Kapadia, Sujit, 2010. "Contagion in financial networks," Bank of England working papers 383, Bank of England.
    4. Caccioli, Fabio & Shrestha, Munik & Moore, Cristopher & Farmer, J. Doyne, 2014. "Stability analysis of financial contagion due to overlapping portfolios," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 233-245.
    5. Yannick Armenti & Stéphane Crépey & Samuel Drapeau & Antonis Papapantoleon, 2018. "Multivariate Shortfall Risk Allocation and Systemic Risk," Working Papers hal-01764398, HAL.
    6. T. R. Hurd & Davide Cellai & Sergey Melnik & Quentin H. Shao, 2016. "Double Cascade Model Of Financial Crises," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-27, August.
    7. Battiston, Stefano & Delli Gatti, Domenico & Gallegati, Mauro & Greenwald, Bruce & Stiglitz, Joseph E., 2012. "Liaisons dangereuses: Increasing connectivity, risk sharing, and systemic risk," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1121-1141.
    8. Rama Cont & Amal Moussa & Edson B Santos, 2013. "Network structure and systemic risk in banking systems," Post-Print hal-00912018, HAL.
    9. Hamed Amini & Rama Cont & Andreea Minca, 2016. "Resilience To Contagion In Financial Networks," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 329-365, April.
    10. Seung Hwan Lee, 2013. "Systemic Liquidity Shortages and Interbank Network Structures," Working Papers 2013-4, Economic Research Institute, Bank of Korea.
    11. Thomas R. Hurd & Davide Cellai & Sergey Melnik & Quentin Shao, 2013. "Double Cascade Model of Financial Crises," Papers 1310.6873, arXiv.org, revised Sep 2016.
    12. Fabio Bellini & Marco Frittelli, 2002. "On the Existence of Minimax Martingale Measures," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 1-21, January.
    13. L. C. G. Rogers & L. A. M. Veraart, 2013. "Failure and Rescue in an Interbank Network," Management Science, INFORMS, vol. 59(4), pages 882-898, April.
    14. Markus K. Brunnermeier & Patrick Cheridito, 2019. "Measuring and Allocating Systemic Risk," Risks, MDPI, vol. 7(2), pages 1-19, April.
    15. Rodrigo Cifuentes & Hyun Song Shin & Gianluigi Ferrucci, 2005. "Liquidity Risk and Contagion," Journal of the European Economic Association, MIT Press, vol. 3(2-3), pages 556-566, 04/05.
    16. Hamed Amini & Damir Filipović & Andreea Minca, 2013. "Systemic Risk and Central Clearing Counterparty Design," Swiss Finance Institute Research Paper Series 13-34, Swiss Finance Institute.
    17. Sara Biagini & Marco Frittelli, 2005. "Utility maximization in incomplete markets for unbounded processes," Finance and Stochastics, Springer, vol. 9(4), pages 493-517, October.
    18. 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.
    19. Patrick Cheridito & Tianhui Li, 2009. "Risk Measures On Orlicz Hearts," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 189-214, April.
    20. Larry Eisenberg & Thomas H. Noe, 2001. "Systemic Risk in Financial Systems," Management Science, INFORMS, vol. 47(2), pages 236-249, February.
    21. Lee, Seung Hwan, 2013. "Systemic liquidity shortages and interbank network structures," Journal of Financial Stability, Elsevier, vol. 9(1), pages 1-12.
    22. Michael Boss & Helmut Elsinger & Martin Summer & Stefan Thurner, 2004. "Network topology of the interbank market," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 677-684.
    23. Chen Chen & Garud Iyengar & Ciamac C. Moallemi, 2013. "An Axiomatic Approach to Systemic Risk," Management Science, INFORMS, vol. 59(6), pages 1373-1388, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Alessandro Doldi & Marco Frittelli, 2020. "Conditional Systemic Risk Measures," Papers 2010.11515, arXiv.org, revised May 2021.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alessandro Doldi & Marco Frittelli, 2021. "Real-Valued Systemic Risk Measures," Mathematics, MDPI, vol. 9(9), pages 1-24, April.
    2. T. R. Hurd, 2018. "Bank Panics And Fire Sales, Insolvency And Illiquidity," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(06), pages 1-30, September.
    3. Marco Bardoscia & Paolo Barucca & Stefano Battiston & Fabio Caccioli & Giulio Cimini & Diego Garlaschelli & Fabio Saracco & Tiziano Squartini & Guido Caldarelli, 2021. "The Physics of Financial Networks," Papers 2103.05623, arXiv.org.
    4. Sadamori Kojaku & Giulio Cimini & Guido Caldarelli & Naoki Masuda, 2018. "Structural changes in the interbank market across the financial crisis from multiple core-periphery analysis," Papers 1802.05139, arXiv.org.
    5. Brandi, Giuseppe & Di Clemente, Riccardo & Cimini, Giulio, 2018. "Epidemics of liquidity shortages in interbank markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 255-267.
    6. Fabio Caccioli & Paolo Barucca & Teruyoshi Kobayashi, 2018. "Network models of financial systemic risk: a review," Journal of Computational Social Science, Springer, vol. 1(1), pages 81-114, January.
    7. Hüser, Anne-Caroline, 2016. "Too interconnected to fail: A survey of the Interbank Networks literature," SAFE Working Paper Series 91, Leibniz Institute for Financial Research SAFE, revised 2016.
    8. T. R. Hurd & Davide Cellai & Sergey Melnik & Quentin H. Shao, 2016. "Double Cascade Model Of Financial Crises," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-27, August.
    9. Hamed Amini & Andreea Minca, 2016. "Inhomogeneous Financial Networks and Contagious Links," Operations Research, INFORMS, vol. 64(5), pages 1109-1120, October.
    10. Paul Glasserman & H. Peyton Young, 2015. "Contagion in Financial Markets," Working Papers 15-21, Office of Financial Research, US Department of the Treasury.
    11. Paul Glasserman & Peyton Young, 2015. "Contagion in Financial Networks," Economics Series Working Papers 764, University of Oxford, Department of Economics.
    12. Morteza Alaeddini & Philippe Madiès & Paul J. Reaidy & Julie Dugdale, 2023. "Interbank money market concerns and actors’ strategies—A systematic review of 21st century literature," Journal of Economic Surveys, Wiley Blackwell, vol. 37(2), pages 573-654, April.
    13. Valentina Macchiati & Giuseppe Brandi & Tiziana Di Matteo & Daniela Paolotti & Guido Caldarelli & Giulio Cimini, 2022. "Systemic liquidity contagion in the European interbank market," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(2), pages 443-474, April.
    14. Covi, Giovanni & Gorpe, Mehmet Ziya & Kok, Christoffer, 2021. "CoMap: Mapping Contagion in the Euro Area Banking Sector," Journal of Financial Stability, Elsevier, vol. 53(C).
    15. Carro, Adrian & Stupariu, Patricia, 2024. "Uncertainty, non-linear contagion and the credit quality channel: An application to the Spanish interbank market," Journal of Financial Stability, Elsevier, vol. 71(C).
    16. Gandy, Axel & Veraart, Luitgard A. M., 2021. "Compound poisson models for weighted networks with applications in finance," LSE Research Online Documents on Economics 104185, London School of Economics and Political Science, LSE Library.
    17. Wiersema, Garbrand & Kleinnijenhuis, Alissa M. & Wetzer, Thom & Farmer, J. Doyne, 2023. "Scenario-free analysis of financial stability with interacting contagion channels," Journal of Banking & Finance, Elsevier, vol. 146(C).
    18. Kerstin Awiszus & Agostino Capponi & Stefan Weber, 2020. "Market Efficient Portfolios in a Systemic Economy," Papers 2003.10121, arXiv.org, revised May 2021.
    19. Nils Detering & Thilo Meyer-Brandis & Konstantinos Panagiotou & Daniel Ritter, 2020. "Suffocating Fire Sales," Papers 2006.08110, arXiv.org, revised Nov 2021.
    20. Yichen Zhou & Honggang Li, 2019. "Asset diversification and systemic risk in the financial system," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(2), pages 247-272, June.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:finsto:v:24:y:2020:i:2:d:10.1007_s00780-020-00417-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.