IDEAS home Printed from https://ideas.repec.org/p/una/unccee/wp1506.html
   My bibliography  Save this paper

On a relationship between distorted and spectral risk measures

Author

Listed:
  • Henryk Gzyl

    (Centro de Finanzas, IESA)

  • Silvia Mayoral

    (Universidad de Navarra)

Abstract

We study the relationship between two widely used risk measures, spectral measures and distortion risk measures. In both cases, the risk measure can be thought of as a re-weighting of some initial distribution. We prove that spectral risk measures are equivalent to distorted risk pricing measures, or equivalently, spectral risk functions are equivalent to distortion functions. Besides, we prove that distorted measures are absolutely continuous with respect to the original measure. This allows us to find a link between the risk measures based on relative entropy and spectral risk measures or measures based on distortion risk functions.

Suggested Citation

  • Henryk Gzyl & Silvia Mayoral, 2006. "On a relationship between distorted and spectral risk measures," Faculty Working Papers 15/06, School of Economics and Business Administration, University of Navarra.
    • Handle: RePEc:una:unccee:wp1506
    as

    Download full text from publisher

    File URL: http://www.unav.edu/documents/10174/6546776/1187093368_Gzyl_Mayoral.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Cotter, John & Dowd, Kevin, 2006. "Extreme spectral risk measures: An application to futures clearinghouse margin requirements," Journal of Banking & Finance, Elsevier, vol. 30(12), pages 3469-3485, December.
    2. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
    3. Gourieroux, C. & Laurent, J. P. & Scaillet, O., 2000. "Sensitivity analysis of Values at Risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 225-245, November.
    4. Acerbi Carlo & Simonetti Prospero, 2002. "Portfolio Optimization with Spectral Measures of Risk," Papers cond-mat/0203607, arXiv.org.
    5. 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.
    6. Werner Hürlimann, 2004. "Distortion Risk Measures and Economic Capital," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(1), pages 86-95.
    7. Goovaerts, Marc J. & Laeven, Roger J.A., 2008. "Actuarial risk measures for financial derivative pricing," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 540-547, April.
    8. Wang, Shaun S. & Young, Virginia R. & Panjer, Harry H., 1997. "Axiomatic characterization of insurance prices," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 173-183, November.
    9. 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.
    10. Schweizer, Martin, 2001. "From actuarial to financial valuation principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 31-47, February.
    11. Hurlimann, Werner, 2001. "Distribution-free comparison of pricing principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 351-360, 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. Liu, Yangyang & Zhou, Jiangxin & Zhou, Qihui & Liu, Chuanquan & Yu, Feng, 2023. "Bidding strategy of integrated energy system considering decision maker’s subjective risk aversion," Applied Energy, Elsevier, vol. 341(C).
    2. Gzyl, Henryk & Mayoral, Silvia, 2008. "Determination of risk pricing measures from market prices of risk," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 437-443, December.

    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. Boonen, Tim J., 2017. "Risk Redistribution Games With Dual Utilities," ASTIN Bulletin, Cambridge University Press, vol. 47(1), pages 303-329, January.
    2. Gzyl, Henryk & Mayoral, Silvia, 2008. "Determination of risk pricing measures from market prices of risk," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 437-443, December.
    3. Mario Brandtner, 2016. "Spektrale Risikomaße: Konzeption, betriebswirtschaftliche Anwendungen und Fallstricke," Management Review Quarterly, Springer, vol. 66(2), pages 75-115, April.
    4. Wentao Hu & Cuixia Chen & Yufeng Shi & Ze Chen, 2022. "A Tail Measure With Variable Risk Tolerance: Application in Dynamic Portfolio Insurance Strategy," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 831-874, June.
    5. Stelios Bekiros & Nikolaos Loukeris & Iordanis Eleftheriadis & Christos Avdoulas, 2019. "Tail-Related Risk Measurement and Forecasting in Equity Markets," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 783-816, February.
    6. Albrecht, Peter & Huggenberger, Markus, 2017. "The fundamental theorem of mutual insurance," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 180-188.
    7. Wächter, Hans Peter & Mazzoni, Thomas, 2013. "Consistent modeling of risk averse behavior with spectral risk measures," European Journal of Operational Research, Elsevier, vol. 229(2), pages 487-495.
    8. James Ming Chen, 2018. "On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles," Risks, MDPI, vol. 6(2), pages 1-28, June.
    9. Dirk Tasche, 2002. "Expected Shortfall and Beyond," Papers cond-mat/0203558, arXiv.org, revised Oct 2002.
    10. Andreas Tsanakas & Pietro Millossovich, 2016. "Sensitivity Analysis Using Risk Measures," Risk Analysis, John Wiley & Sons, vol. 36(1), pages 30-48, January.
    11. Choo, Weihao & de Jong, Piet, 2009. "Loss reserving using loss aversion functions," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 271-277, October.
    12. Adam, Alexandre & Houkari, Mohamed & Laurent, Jean-Paul, 2008. "Spectral risk measures and portfolio selection," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1870-1882, September.
    13. Denuit Michel & Dhaene Jan & Goovaerts Marc & Kaas Rob & Laeven Roger, 2006. "Risk measurement with equivalent utility principles," Statistics & Risk Modeling, De Gruyter, vol. 24(1), pages 1-25, July.
    14. Fasen Vicky & Svejda Adela, 2012. "Time consistency of multi-period distortion measures," Statistics & Risk Modeling, De Gruyter, vol. 29(2), pages 133-153, June.
    15. Tasche, Dirk, 2002. "Expected shortfall and beyond," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1519-1533, July.
    16. Gao, Huan & Mamon, Rogemar & Liu, Xiaoming, 2017. "Risk measurement of a guaranteed annuity option under a stochastic modelling framework," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 100-119.
    17. Christian Gourieroux & Wei Liu, 2006. "Sensitivity Analysis of Distortion Risk Measures," Working Papers 2006-33, Center for Research in Economics and Statistics.
    18. Holly Brannelly & Andrea Macrina & Gareth W. Peters, 2021. "Stochastic measure distortions induced by quantile processes for risk quantification and valuation," Papers 2201.02045, arXiv.org.
    19. 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.
    20. Choo, Weihao & de Jong, Piet, 2015. "The tradeoff insurance premium as a two-sided generalisation of the distortion premium," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 238-246.

    More about this item

    Keywords

    Coherent risk measure; Distortion function; Spectral measures; risk aversion function.Spectral measu;
    All these keywords.

    JEL classification:

    • J13 - Labor and Demographic Economics - - Demographic Economics - - - Fertility; Family Planning; Child Care; Children; Youth

    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:una:unccee:wp1506. 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: the person in charge (email available below). General contact details of provider: http://www.unav.edu/web/facultad-de-ciencias-economicas-y-empresariales .

    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.