IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v42y2008i3p1022-1027.html
   My bibliography  Save this article

Tolerance intervals for quantiles of bivariate risks and risk measurement

Author

Listed:
  • Gebizlioglu, Omer L.
  • Yagci, Banu

Abstract

This paper considers joint distributions of order statistics for risk variables and their concomitants for actuarial risk analysis under dependence. With this purpose, bivariate integral transformations are performed and some examples are presented using copulas, the FGM copulas in particular. Quantiles of the distributions concerned are discussed and their tolerance intervals are constructed. Risk measures such as VaR in the set up of the tolerance intervals are included in the discussions.

Suggested Citation

  • Gebizlioglu, Omer L. & Yagci, Banu, 2008. "Tolerance intervals for quantiles of bivariate risks and risk measurement," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1022-1027, June.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:3:p:1022-1027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-6687(07)00139-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Tank, Fatih & Gebizlioglu, Omer L. & Apaydin, Aysen, 2006. "Determination of dependency parameter in joint distribution of dependent risks by fuzzy approach," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 189-194, February.
    2. Chen, L. -A. & Welsh, A. H., 2002. "Distribution-Function-Based Bivariate Quantiles," Journal of Multivariate Analysis, Elsevier, vol. 83(1), pages 208-231, October.
    3. Denuit, M. & Genest, C. & Marceau, E., 1999. "Stochastic bounds on sums of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 85-104, September.
    4. Rodríguez-Lallena, José A. & Úbeda-Flores, Manuel, 2003. "Distribution functions of multivariate copulas," Statistics & Probability Letters, Elsevier, vol. 64(1), pages 41-50, August.
    5. I. Bairamov & S. Kotz & M. Bekci, 2001. "New generalized Farlie-Gumbel-Morgenstern distributions and concomitants of order statistics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(5), pages 521-536.
    6. Nelsen, Roger B. & Quesada-Molina, José Juan & Rodríguez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2001. "Distribution functions of copulas: a class of bivariate probability integral transforms," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 277-282, October.
    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. Buch-Kromann, Tine & Guillén, Montserrat & Linton, Oliver & Nielsen, Jens Perch, 2011. "Multivariate density estimation using dimension reducing information and tail flattening transformations," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 99-110, January.
    2. Pitselis, Georgios, 2013. "Quantile credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 477-489.
    3. Fernández, Arturo J., 2010. "Two-sided tolerance intervals in the exponential case: Corrigenda and generalizations," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 151-162, January.
    4. Pitselis, Georgios, 2020. "Multi-stage nested classification credibility quantile regression model," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 162-176.

    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. Kemaloglu, Sibel Acik & Shapiro, Arnold F. & Tank, Fatih & Apaydin, Aysen, 2018. "Using fuzzy logic to interpret dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 101-106.
    2. Bolancé, Catalina & Bahraoui, Zuhair & Artís, Manuel, 2014. "Quantifying the risk using copulae with nonparametric marginals," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 46-56.
    3. Mansour Shrahili & Mohamed Kayid, 2023. "Stochastic Orderings of the Idle Time of Inactive Standby Systems," Mathematics, MDPI, vol. 11(20), pages 1-21, October.
    4. Paul Embrechts & Giovanni Puccetti, 2006. "Bounds for Functions of Dependent Risks," Finance and Stochastics, Springer, vol. 10(3), pages 341-352, September.
    5. Serguei Foss & Andrew Richards, 2010. "On Sums of Conditionally Independent Subexponential Random Variables," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 102-119, February.
    6. Thibaut Lux & Antonis Papapantoleon, 2016. "Model-free bounds on Value-at-Risk using extreme value information and statistical distances," Papers 1610.09734, arXiv.org, revised Nov 2018.
    7. Embrechts, Paul & Hoing, Andrea & Puccetti, Giovanni, 2005. "Worst VaR scenarios," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 115-134, August.
    8. Puccetti Giovanni & Rüschendorf Ludger, 2012. "Bounds for joint portfolios of dependent risks," Statistics & Risk Modeling, De Gruyter, vol. 29(2), pages 107-132, June.
    9. Nelsen, Roger B. & Quesada-Molina, José Juan & Rodri­guez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2008. "On the construction of copulas and quasi-copulas with given diagonal sections," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 473-483, April.
    10. Mihai Banciu & Fredrik Ødegaard & Alia Stanciu, 2019. "Distribution-free bounds for the expected marginal seat revenue heuristic with dependent demands," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 18(2), pages 155-163, April.
    11. Karishma Ansaram & Paolo Mazza, 2022. "Dependence structure among carbon markets around the world: New evidence from GARCH-copula analysis," Working Papers 2022-ACF-03, IESEG School of Management.
    12. Kaas, Rob & Laeven, Roger J.A. & Nelsen, Roger B., 2009. "Worst VaR scenarios with given marginals and measures of association," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 146-158, April.
    13. Shih, Jia-Han & Emura, Takeshi, 2021. "On the copula correlation ratio and its generalization," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    14. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel & Jing Yao, 2017. "How robust is the value-at-risk of credit risk portfolios?," The European Journal of Finance, Taylor & Francis Journals, vol. 23(6), pages 507-534, May.
    15. Lux, Thibaut & Papapantoleon, Antonis, 2019. "Model-free bounds on Value-at-Risk using extreme value information and statistical distances," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 73-83.
    16. Cherubini, Umberto & Mulinacci, Sabrina & Romagnoli, Silvia, 2011. "On the distribution of the (un)bounded sum of random variables," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 56-63, January.
    17. Corrado De Vecchi & Max Nendel & Jan Streicher, 2024. "Upper Comonotonicity and Risk Aggregation under Dependence Uncertainty," Papers 2406.19242, arXiv.org.
    18. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    19. Laeven, Roger J.A., 2009. "Worst VaR scenarios: A remark," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 159-163, April.
    20. Bernard, Carole & Vanduffel, Steven, 2015. "A new approach to assessing model risk in high dimensions," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 166-178.

    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:eee:insuma:v:42:y:2008:i:3:p:1022-1027. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.