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Supermodular dependence ordering on a class of multivariate copulas

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  • Wei, Gang
  • Hu, Taizhong

Abstract

In most situations, the dependence monotonicities of copulas are checked by problem-specific approaches. Sometimes, it is impossible to check the monotonicities from the analytic forms of copulas. The purpose of this paper is to lay out some general results that can be used to identify dependence parameter(s) with respect to the supermodular dependence ordering for a parametric family of copulas constructed through mixing and limits. Special attention is paid to multivariate extreme value copulas, and some examples of applications are provided.

Suggested Citation

  • Wei, Gang & Hu, Taizhong, 2002. "Supermodular dependence ordering on a class of multivariate copulas," Statistics & Probability Letters, Elsevier, vol. 57(4), pages 375-385, May.
    • Handle: RePEc:eee:stapro:v:57:y:2002:i:4:p:375-385
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    References listed on IDEAS

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    Cited by:

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    4. Georg Mainik & Ludger Ruschendorf, 2010. "Ordering of multivariate probability distributions with respect to extreme portfolio losses," Papers 1010.5171, arXiv.org.
    5. Georg Mainik & Eric Schaanning, 2012. "On dependence consistency of CoVaR and some other systemic risk measures," Papers 1207.3464, arXiv.org, revised Aug 2012.
    6. Müller, Alfred & Scarsini, Marco, 2005. "Archimedean copulæ and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 434-445, April.
    7. Masih-Tehrani, Behdad & Xu, Susan H. & Kumara, Soundar & Li, Haijun, 2011. "A single-period analysis of a two-echelon inventory system with dependent supply uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 45(8), pages 1128-1151, September.
    8. Christian Genest & Johanna Nešlehová & Johanna Ziegel, 2011. "Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 223-256, August.
    9. Cossette, Hélène & Marceau, Etienne & Mtalai, Itre, 2019. "Collective risk models with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 153-168.
    10. Areski Cousin & Elena Di Bernadino, 2013. "On Multivariate Extensions of Value-at-Risk," Working Papers hal-00638382, HAL.
    11. Mainik Georg & Schaanning Eric, 2014. "On dependence consistency of CoVaRand some other systemic risk measures," Statistics & Risk Modeling, De Gruyter, vol. 31(1), pages 49-77, March.
    12. Cossette, Hélène & Marceau, Etienne & Trufin, Julien & Zuyderhoff, Pierre, 2020. "Ruin-based risk measures in discrete-time risk models," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 246-261.
    13. Mainik Georg & Rüschendorf Ludger, 2012. "Ordering of multivariate risk models with respect to extreme portfolio losses," Statistics & Risk Modeling, De Gruyter, vol. 29(1), pages 73-106, March.
    14. Genest, Christian & Marceau, Etienne & Mesfioui, Mhamed, 2003. "Compound Poisson approximations for individual models with dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 73-91, February.
    15. Rüschendorf Ludger & Witting Julian, 2017. "VaR bounds in models with partial dependence information on subgroups," Dependence Modeling, De Gruyter, vol. 5(1), pages 59-74, January.
    16. Damiano Brigo & Kyriakos Chourdakis, 2012. "Consistent single- and multi-step sampling of multivariate arrival times: A characterization of self-chaining copulas," Papers 1204.2090, arXiv.org, revised Apr 2012.
    17. Embrechts, Paul & Neslehová, Johanna & Wüthrich, Mario V., 2009. "Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 164-169, April.
    18. Huang, Jen-Jsung & Lee, Kuo-Jung & Liang, Hueimei & Lin, Wei-Fu, 2009. "Estimating value at risk of portfolio by conditional copula-GARCH method," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 315-324, December.
    19. Di Bernardino, E. & Fernández-Ponce, J.M. & Palacios-Rodríguez, F. & Rodríguez-Griñolo, M.R., 2015. "On multivariate extensions of the conditional Value-at-Risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 1-16.
    20. Areski Cousin & Elena Di Bernadino, 2011. "On Multivariate Extensions of Value-at-Risk," Papers 1111.1349, arXiv.org, revised Apr 2013.
    21. Cousin, Areski & Di Bernardino, Elena, 2013. "On multivariate extensions of Value-at-Risk," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 32-46.

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