IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v172y2019icp28-46.html
   My bibliography  Save this article

Dependence in a background risk model

Author

Listed:
  • Côté, Marie-Pier
  • Genest, Christian

Abstract

Many copula families, including the classes of Archimedean, elliptical and Liouville copulas, may be written as the survival copula of a random vector R×(Y1,Y2), where R is a strictly positive random variable independent of the random vector (Y1,Y2) . A unified framework is presented for studying the dependence structure underlying this stochastic representation, which is called the background risk model. Formulas for the copula, Kendall’s tau and tail dependence coefficients are obtained and special cases are detailed. The usefulness of the construction for model building is illustrated with an extension of Archimedean copulas with completely monotone generators, based on the Farlie–Gumbel–Morgenstern copula. In particular, explicit expressions for the distribution and the Tail-Value-at-Risk of the aggregated risk RY1+RY2 are available in a generalization of the widely used multivariate Pareto-II model.

Suggested Citation

  • Côté, Marie-Pier & Genest, Christian, 2019. "Dependence in a background risk model," Journal of Multivariate Analysis, Elsevier, vol. 172(C), pages 28-46.
    • Handle: RePEc:eee:jmvana:v:172:y:2019:i:c:p:28-46
    DOI: 10.1016/j.jmva.2018.11.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X18301477
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2018.11.012?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 search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mercè Claramunt, M. & Lefèvre, Claude & Loisel, Stéphane & Montesinos, Pierre, 2022. "Basis risk management and randomly scaled uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 123-139.
    2. Eric C. K. Cheung & Oscar Peralta & Jae-Kyung Woo, 2021. "Multivariate matrix-exponential affine mixtures and their applications in risk theory," Papers 2201.11122, arXiv.org.
    3. Claude Lefèvre & Stéphane Loisel & Pierre Montesinos, 2020. "Bounding basis risk using s-convex orders on Beta-unimodal distributions," Working Papers hal-02611208, HAL.
    4. Fouad Marri & Khouzeima Moutanabbir, 2021. "Risk aggregation and capital allocation using a new generalized Archimedean copula," Working Papers hal-03169291, HAL.
    5. Moreno Bevilacqua & Christian Caamaño-Carrillo & Reinaldo B. Arellano-Valle & Camilo Gómez, 2022. "A class of random fields with two-piece marginal distributions for modeling point-referenced data with spatial outliers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 644-674, September.
    6. Furman, Edward & Kye, Yisub & Su, Jianxi, 2021. "Multiplicative background risk models: Setting a course for the idiosyncratic risk factors distributed phase-type," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 153-167.
    7. Fouad Marri & Khouzeima Moutanabbir, 2021. "Risk aggregation and capital allocation using a new generalized Archimedean copula," Papers 2103.10989, arXiv.org.
    8. Marri, Fouad & Moutanabbir, Khouzeima, 2022. "Risk aggregation and capital allocation using a new generalized Archimedean copula," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 75-90.
    9. Cheung, Eric C.K. & Peralta, Oscar & Woo, Jae-Kyung, 2022. "Multivariate matrix-exponential affine mixtures and their applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 364-389.
    10. Michel Denuit & Christian Y. Robert, 2022. "Conditional Tail Expectation Decomposition and Conditional Mean Risk Sharing for Dependent and Conditionally Independent Losses," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1953-1985, September.

    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:jmvana:v:172:y:2019:i:c:p:28-46. 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.

    We have no bibliographic references for this item. You can help adding them by using 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.