IDEAS home Printed from https://ideas.repec.org/a/bla/jrinsu/v75y2008i2p365-386.html
   My bibliography  Save this article

Can a Coherent Risk Measure Be Too Subadditive?

Author

Listed:
  • J. Dhaene
  • R. J. A. Laeven
  • S. Vanduffel
  • G. Darkiewicz
  • M. J. Goovaerts

Abstract

We consider the problem of determining appropriate solvency capital requirements for an insurance company or a financial institution. We demonstrate that the subadditivity condition that is often imposed on solvency capital principles can lead to the undesirable situation where the shortfall risk increases by a merger. We propose to complement the subadditivity condition by a regulator's condition. We find that for an explicitly specified confidence level, the Value‐at‐Risk satisfies the regulator's condition and is the “most efficient” capital requirement in the sense that it minimizes some reasonable cost function. Within the class of concave distortion risk measures, of which the elements, in contrast to the Value‐at‐Risk, exhibit the subadditivity property, we find that, again for an explicitly specified confidence level, the Tail‐Value‐at‐Risk is the optimal capital requirement satisfying the regulator's condition.

Suggested Citation

  • J. Dhaene & R. J. A. Laeven & S. Vanduffel & G. Darkiewicz & M. J. Goovaerts, 2008. "Can a Coherent Risk Measure Be Too Subadditive?," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 365-386, June.
    • Handle: RePEc:bla:jrinsu:v:75:y:2008:i:2:p:365-386
    DOI: 10.1111/j.1539-6975.2008.00264.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1539-6975.2008.00264.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1539-6975.2008.00264.x?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
    ---><---

    References listed on IDEAS

    as
    1. Casper G. de Vries & Gennady Samorodnitsky & Bjørn N. Jorgensen & Sarma Mandira & Jon Danielsson, 2005. "Subadditivity Re–Examined: the Case for Value-at-Risk," FMG Discussion Papers dp549, Financial Markets Group.
    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. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2013. "A comparison of the original and revised Basel market risk frameworks for regulating bank capital," Journal of Economic Behavior & Organization, Elsevier, vol. 85(C), pages 249-268.
    2. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2012. "When more is less: Using multiple constraints to reduce tail risk," Journal of Banking & Finance, Elsevier, vol. 36(10), pages 2693-2716.
    3. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel & Ruodu Wang, 2017. "Risk bounds for factor models," Finance and Stochastics, Springer, vol. 21(3), pages 631-659, July.
    4. Lazar, Emese & Zhang, Ning, 2019. "Model risk of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 74-93.
    5. Gaglianone, Wagner Piazza & Lima, Luiz Renato & Linton, Oliver & Smith, Daniel R., 2011. "Evaluating Value-at-Risk Models via Quantile Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 150-160.
    6. Hofert, Marius & McNeil, Alexander J., 2015. "Subadditivity of Value-at-Risk for Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 79-88.
    7. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524, January.
    8. repec:hal:journl:hal-00880258 is not listed on IDEAS
    9. Szüle, Borbála, 2010. "Biztosítók kockázatdiverzifikációja [Risk diversification of insurers]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 634-651.
    10. Babat, Onur & Vera, Juan C. & Zuluaga, Luis F., 2018. "Computing near-optimal Value-at-Risk portfolios using integer programming techniques," European Journal of Operational Research, Elsevier, vol. 266(1), pages 304-315.
    11. Daníelsson, Jón & Jorgensen, Bjørn N. & Samorodnitsky, Gennady & Sarma, Mandira & de Vries, Casper G., 2013. "Fat tails, VaR and subadditivity," Journal of Econometrics, Elsevier, vol. 172(2), pages 283-291.
    12. Jaume Belles‐Sampera & Montserrat Guillén & Miguel Santolino, 2014. "Beyond Value‐at‐Risk: GlueVaR Distortion Risk Measures," Risk Analysis, John Wiley & Sons, vol. 34(1), pages 121-134, January.
    13. Georg Mainik & Ludger Rüschendorf, 2010. "On optimal portfolio diversification with respect to extreme risks," Finance and Stochastics, Springer, vol. 14(4), pages 593-623, December.
    14. Albert J Menkveld, 2017. "Crowded Positions: An Overlooked Systemic Risk for Central Clearing Parties," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 7(2), pages 209-242.
    15. Genest, Christian & Gerber, Hans U. & Goovaerts, Marc J. & Laeven, Roger J.A., 2009. "Editorial to the special issue on modeling and measurement of multivariate risk in insurance and finance," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 143-145, April.
    16. Oliver Kley & Claudia Kluppelberg & Gesine Reinert, 2014. "Risk in a large claims insurance market with bipartite graph structure," Papers 1410.8671, arXiv.org, revised Nov 2015.
    17. Geenens, Gery & Dunn, Richard, 2022. "A nonparametric copula approach to conditional Value-at-Risk," Econometrics and Statistics, Elsevier, vol. 21(C), pages 19-37.
    18. Kratz , Marie, 2013. "There is a VaR Beyond Usual Approximations," ESSEC Working Papers WP1317, ESSEC Research Center, ESSEC Business School.
    19. Bakshi, Gurdip & Panayotov, George, 2010. "First-passage probability, jump models, and intra-horizon risk," Journal of Financial Economics, Elsevier, vol. 95(1), pages 20-40, January.
    20. J. D. Opdyke, 2014. "Estimating Operational Risk Capital with Greater Accuracy, Precision, and Robustness," Papers 1406.0389, arXiv.org, revised Nov 2014.
    21. Dominique Guegan & Bertrand K Hassani, 2014. "Distortion Risk Measures or the Transformation of Unimodal Distributions into Multimodal Functions," Documents de travail du Centre d'Economie de la Sorbonne 14008, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

    More about this item

    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:bla:jrinsu:v:75:y:2008:i:2:p:365-386. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/ariaaea.html .

    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.