IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v74y2011i2p267-285.html

Rates of almost sure convergence of plug-in estimates for distortion risk measures

Author

Listed:
  • Henryk Zähle

Abstract

No abstract is available for this item.

Suggested Citation

  • Henryk Zähle, 2011. "Rates of almost sure convergence of plug-in estimates for distortion risk measures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(2), pages 267-285, September.
    • Handle: RePEc:spr:metrik:v:74:y:2011:i:2:p:267-285
    DOI: 10.1007/s00184-010-0302-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00184-010-0302-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00184-010-0302-z?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

    for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Bruce Jones & Ričardas Zitikis, 2003. "Empirical Estimation of Risk Measures and Related Quantities," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 44-54.
    3. Song Xi Chen, 2008. "Nonparametric Estimation of Expected Shortfall," Journal of Financial Econometrics, Oxford University Press, vol. 6(1), pages 87-107, Winter.
    4. Galen R. Shorack, 1979. "The weighted empirical process of row independent random variables with arbitrary distribution functions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 33(4), pages 169-189, December.
    5. 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.
    6. Carlo Acerbi & Dirk Tasche, 2002. "Expected Shortfall: A Natural Coherent Alternative to Value at Risk," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 31(2), pages 379-388, July.
    7. repec:cup:astinb:v:26:y:1996:i:01:p:71-92_00 is not listed on IDEAS
    8. Jones, Bruce L. & Zitikis, Ricardas, 2007. "Risk measures, distortion parameters, and their empirical estimation," Insurance: Mathematics and Economics, Elsevier, vol. 41(2), pages 279-297, September.
    9. David Wozabal & Nancy Wozabal, 2009. "Asymptotic consistency of risk functionals," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(8), pages 977-990.
    10. Jones, Bruce L. & Puri, Madan L. & Zitikis, Ricardas, 2006. "Testing hypotheses about the equality of several risk measure values with applications in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 253-270, April.
    11. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    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. Georg Pflug & Nancy Wozabal, 2010. "Asymptotic distribution of law-invariant risk functionals," Finance and Stochastics, Springer, vol. 14(3), pages 397-418, September.
    2. Psarrakos, Georgios & Sordo, Miguel A., 2019. "On a family of risk measures based on proportional hazards models and tail probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 232-240.
    3. Domagoj Demeterfi & Kathrin Glau & Linus Wunderlich, 2025. "Function approximations for counterparty credit exposure calculations," Papers 2507.09004, arXiv.org.
    4. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2015. "Shortfall Deviation Risk: An alternative to risk measurement," Papers 1501.02007, arXiv.org, revised May 2016.
    5. Massimiliano Amarante, 2016. "A representation of risk measures," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(1), pages 95-103, April.
    6. Ruodu Wang & Ričardas Zitikis, 2021. "An Axiomatic Foundation for the Expected Shortfall," Management Science, INFORMS, vol. 67(3), pages 1413-1429, March.
    7. De Giorgi, Enrico, 2005. "Reward-risk portfolio selection and stochastic dominance," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 895-926, April.
    8. Labopin-Richard T. & Gamboa F. & Garivier A. & Iooss B., 2016. "Bregman superquantiles. Estimation methods and applications," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-33, March.
    9. Ardakani, Omid M., 2023. "Coherent measure of portfolio risk," Finance Research Letters, Elsevier, vol. 57(C).
    10. Cameron A. MacKenzie, 2014. "Summarizing Risk Using Risk Measures and Risk Indices," Risk Analysis, John Wiley & Sons, vol. 34(12), pages 2143-2162, December.
    11. Gregor Dorfleitner, 2022. "On the use of the terminal-value approach in risk-value models," Annals of Operations Research, Springer, vol. 313(2), pages 877-897, June.
    12. Kim, Joseph H.T., 2010. "Bias correction for estimated distortion risk measure using the bootstrap," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 198-205, October.
    13. Brandtner, Mario, 2013. "Conditional Value-at-Risk, spectral risk measures and (non-)diversification in portfolio selection problems – A comparison with mean–variance analysis," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5526-5537.
    14. Darinka Dentcheva & Spiridon Penev & Andrzej Ruszczyński, 2017. "Statistical estimation of composite risk functionals and risk optimization problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 737-760, August.
    15. Christopher Blier-Wong & Jean-Gabriel Lauzier, 2026. "Designing entry-monotone risk-sharing pools," Papers 2606.00972, arXiv.org.
    16. Giovanni Paolo Crespi & Elisa Mastrogiacomo, 2020. "Qualitative robustness of set-valued value-at-risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 25-54, February.
    17. Brahimi, Brahim & Meraghni, Djamel & Necir, Abdelhakim & Zitikis, Ričardas, 2011. "Estimating the distortion parameter of the proportional-hazard premium for heavy-tailed losses," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 325-334.
    18. 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.
    19. Steven Kou & Xianhua Peng, 2016. "On the Measurement of Economic Tail Risk," Operations Research, INFORMS, vol. 64(5), pages 1056-1072, October.
    20. 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.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    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:metrik:v:74:y:2011:i:2:p:267-285. 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.