IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1602.05477.html
   My bibliography  Save this paper

Which eligible assets are compatible with comonotonic capital requirements?

Author

Listed:
  • Pablo Koch-Medina
  • Cosimo Munari
  • Gregor Svindland

Abstract

Within the context of capital adequacy, we study comonotonicity of risk measures in terms of the primitives of the theory: acceptance sets and eligible, or reference, assets. We show that comonotonicity cannot be characterized by the properties of the acceptance set alone and heavily depends on the choice of the eligible asset. In fact, in many important cases, comonotonicity is only compatible with risk-free eligible assets. The incompatibility with risky eligible assets is systematic whenever the acceptability criterion is based on Value at Risk or any convex distortion risk measure such as Expected Shortfall. These findings qualify and arguably call for a critical appraisal of the meaning and the role of comonotonicity within a capital adequacy context.

Suggested Citation

  • Pablo Koch-Medina & Cosimo Munari & Gregor Svindland, 2016. "Which eligible assets are compatible with comonotonic capital requirements?," Papers 1602.05477, arXiv.org, revised Jan 2021.
    • Handle: RePEc:arx:papers:1602.05477
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1602.05477
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Walter Farkas & Pablo Koch-Medina & Cosimo Munari, 2012. "Capital requirements with defaultable securities," Papers 1203.4610, arXiv.org, revised Jan 2014.
    2. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    3. J. Dhaene & S. Vanduffel & M. Goovaerts, 2007. "Comonotonicity," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(2), pages 265-278.
    4. Artzner, Philippe & Delbaen, Freddy & Koch-Medina, Pablo, 2009. "Risk Measures and Efficient use of Capital 1," ASTIN Bulletin, Cambridge University Press, vol. 39(1), pages 101-116, May.
    5. Farkas, Walter & Koch-Medina, Pablo & Munari, Cosimo, 2014. "Capital requirements with defaultable securities," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 58-67.
    6. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    7. Walter Farkas & Pablo Koch-Medina & Cosimo Munari, 2012. "Beyond cash-additive risk measures: when changing the num\'{e}raire fails," Papers 1206.0478, arXiv.org, revised Feb 2014.
    Full references (including those not matched with items on IDEAS)

    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. Pablo Koch-Medina & Santiago Moreno-Bromberg & Cosimo Munari, 2014. "Capital adequacy tests and limited liability of financial institutions," Papers 1401.3133, arXiv.org, revised Feb 2014.
    2. Andreas H. Hamel & Frank Heyde, 2021. "Set-Valued T -Translative Functions and Their Applications in Finance," Mathematics, MDPI, vol. 9(18), pages 1-33, September.
    3. Andreas H Hamel, 2018. "Monetary Measures of Risk," Papers 1812.04354, arXiv.org.
    4. Laudagé, Christian & Sass, Jörn & Wenzel, Jörg, 2022. "Combining multi-asset and intrinsic risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 254-269.
    5. W. Farkas & A. Smirnow, 2016. "Intrinsic risk measures," Papers 1610.08782, arXiv.org.
    6. Koch-Medina, Pablo & Moreno-Bromberg, Santiago & Munari, Cosimo, 2015. "Capital adequacy tests and limited liability of financial institutions," Journal of Banking & Finance, Elsevier, vol. 51(C), pages 93-102.
    7. Samuel Solgon Santos & Marcelo Brutti Righi & Eduardo de Oliveira Horta, 2022. "The limitations of comonotonic additive risk measures: a literature review," Papers 2212.13864, arXiv.org, revised Jan 2024.
    8. Xue Dong He & Xianhua Peng, 2017. "Surplus-Invariant, Law-Invariant, and Conic Acceptance Sets Must be the Sets Induced by Value-at-Risk," Papers 1707.05596, arXiv.org, revised Jan 2018.
    9. Maria Arduca & Cosimo Munari, 2021. "Risk measures beyond frictionless markets," Papers 2111.08294, arXiv.org.
    10. Fabio Bellini & Pablo Koch-Medina & Cosimo Munari & Gregor Svindland, 2020. "Law-invariant functionals that collapse to the mean," Papers 2009.04144, arXiv.org, revised Jan 2021.
    11. Koch-Medina, Pablo & Munari, Cosimo & Svindland, Gregor, 2018. "Which eligible assets are compatible with comonotonic capital requirements?," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 18-26.
    12. Bellini, Fabio & Koch-Medina, Pablo & Munari, Cosimo & Svindland, Gregor, 2021. "Law-invariant functionals that collapse to the mean," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 83-91.
    13. Chuancun Yin & Dan Zhu, 2015. "New class of distortion risk measures and their tail asymptotics with emphasis on VaR," Papers 1503.08586, arXiv.org, revised Mar 2016.
    14. Cosimo Munari & Stefan Weber & Lutz Wilhelmy, 2023. "Capital requirements and claims recovery: A new perspective on solvency regulation," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 90(2), pages 329-380, June.
    15. Michel Baes & Pablo Koch-Medina & Cosimo Munari, 2017. "Existence, uniqueness and stability of optimal portfolios of eligible assets," Papers 1702.01936, arXiv.org, revised Dec 2017.
    16. Michel Baes & Cosimo Munari, 2020. "A continuous selection for optimal portfolios under convex risk measures does not always exist," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 5-23, February.
    17. Farkas, Walter & Koch-Medina, Pablo & Munari, Cosimo, 2014. "Capital requirements with defaultable securities," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 58-67.
    18. Felix-Benedikt Liebrich & Gregor Svindland, 2018. "Risk sharing for capital requirements with multidimensional security markets," Papers 1809.10015, arXiv.org.
    19. Santos, Samuel S. & Moresco, Marlon R. & Righi, Marcelo B. & Horta, Eduardo, 2024. "A note on the induction of comonotonic additive risk measures from acceptance sets," Statistics & Probability Letters, Elsevier, vol. 208(C).
    20. Michel Baes & Cosimo Munari, 2017. "A continuous selection for optimal portfolios under convex risk measures does not always exist," Papers 1711.00370, arXiv.org.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1602.05477. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.