IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-01171395.html
   My bibliography  Save this paper

Impact of dependence on some multivariate risk indicators

Author

Listed:
  • Véronique Maume-Deschamps

    (ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique, PSPM - Probabilités, statistique, physique mathématique - ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

  • Didier Rullière

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Khalil Said

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon, COACTIS - COnception de l'ACTIon en Situation - UL2 - Université Lumière - Lyon 2 - UJM - Université Jean Monnet - Saint-Étienne)

Abstract

The minimization of some multivariate risk indicators may be used as an allocation method, as proposed in Cénac et al. [6]. The aim of capital allocation is to choose a point in a simplex, according to a given criterion. In a previous paper [17] we proved that the proposed allocation technique satisfies a set of coherence axioms. In the present one, we study the properties and asymptotic behavior of the allocation for some distribution models. We analyze also the impact of the dependence structure on the allocation using some copulas.

Suggested Citation

  • Véronique Maume-Deschamps & Didier Rullière & Khalil Said, 2017. "Impact of dependence on some multivariate risk indicators," Post-Print hal-01171395, HAL.
    • Handle: RePEc:hal:journl:hal-01171395
    DOI: 10.1007/s11009-016-9489-4
    Note: View the original document on HAL open archive server: https://hal.science/hal-01171395
    as

    Download full text from publisher

    File URL: https://hal.science/hal-01171395/document
    Download Restriction: no
    File URL: https://libkey.io/10.1007/s11009-016-9489-4?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Cossette, Hélène & Mailhot, Mélina & Marceau, Étienne, 2012. "TVaR-based capital allocation for multivariate compound distributions with positive continuous claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 247-256.
    2. Cai, Jun & Li, Haijun, 2007. "Dependence properties and bounds for ruin probabilities in multivariate compound risk models," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 757-773, April.
    3. Areski Cousin & Elena Di Bernadino, 2013. "On Multivariate Extensions of Value-at-Risk," Working Papers hal-00638382, HAL.
    4. Cousin, Areski & Di Bernardino, Elena, 2013. "On multivariate extensions of Value-at-Risk," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 32-46.
    5. Peggy Cénac & Stéphane Loisel & Véronique Maume-Deschamps & Clémentine Prieur, 2014. "Risk indicators with several lines of business: comparison, asymptotic behavior and applications to optimal reserve allocation," Post-Print hal-00816894, HAL.
    6. Mathieu Bargès & Hélène Cossette & Etienne Marceau, 2009. "TVaR-based capital allocation with copulas," Working Papers hal-00431265, HAL.
    7. Véronique Maume-Deschamps & Didier Rullière & Khalil Said, 2015. "A risk management approach to capital allocation," Working Papers hal-01163180, HAL.
    8. Elyés Jouini & Moncef Meddeb & Nizar Touzi, 2004. "Vector-valued coherent risk measures," Finance and Stochastics, Springer, vol. 8(4), pages 531-552, November.
    9. Jan Dhaene & Andreas Tsanakas & Emiliano A. Valdez & Steven Vanduffel, 2012. "Optimal Capital Allocation Principles," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(1), pages 1-28, March.
    10. Areski Cousin & Elena Di Bernadino, 2011. "On Multivariate Extensions of Value-at-Risk," Papers 1111.1349, arXiv.org, revised Apr 2013.
    11. repec:dau:papers:123456789/353 is not listed on IDEAS
    12. Bargès, Mathieu & Cossette, Hélène & Marceau, Étienne, 2009. "TVaR-based capital allocation with copulas," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 348-361, December.
    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. Di Bernardino, Elena & Laloë, Thomas & Pakzad, Cambyse, 2024. "Estimation of extreme multivariate expectiles with functional covariates," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    2. Beck, Nicholas & Di Bernardino, Elena & Mailhot, Mélina, 2021. "Semi-parametric estimation of multivariate extreme expectiles," Journal of Multivariate Analysis, Elsevier, vol. 184(C).

    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. repec:hal:wpaper:hal-01171395 is not listed on IDEAS
    2. Cousin, Areski & Di Bernardino, Elena, 2014. "On multivariate extensions of Conditional-Tail-Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 272-282.
    3. Areski Cousin & Elena Di Bernardino, 2013. "On Multivariate Extensions of Conditional-Tail-Expectation," Working Papers hal-00877386, HAL.
    4. Elena Di Bernardino & Clémentine Prieur, 2014. "Estimation of multivariate conditional-tail-expectation using Kendall's process," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(2), pages 241-267, June.
    5. Hélène Cossette & Mélina Mailhot & Étienne Marceau & Mhamed Mesfioui, 2016. "Vector-Valued Tail Value-at-Risk and Capital Allocation," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 653-674, September.
    6. Klaus Herrmann & Marius Hofert & Melina Mailhot, 2017. "Multivariate Geometric Expectiles," Papers 1704.01503, arXiv.org, revised Jan 2018.
    7. Goegebeur, Yuri & Guillou, Armelle & Ho, Nguyen Khanh Le & Qin, Jing, 2023. "A Weissman-type estimator of the conditional marginal expected shortfall," Econometrics and Statistics, Elsevier, vol. 27(C), pages 173-196.
    8. Shuo Gong & Yijun Hu & Linxiao Wei, 2022. "Risk measurement of joint risk of portfolios: a liquidity shortfall aspect," Papers 2212.04848, arXiv.org, revised May 2024.
    9. Matthieu Garcin & Dominique Guegan & Bertrand Hassani, 2017. "A novel multivariate risk measure: the Kendall VaR," Documents de travail du Centre d'Economie de la Sorbonne 17008, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    10. Bazovkin, Pavel, 2014. "Geometrical framework for robust portfolio optimization," Discussion Papers in Econometrics and Statistics 01/14, University of Cologne, Institute of Econometrics and Statistics.
    11. Véronique Maume-Deschamps & Didier Rullière & Khalil Said, 2017. "Multivariate Extensions Of Expectiles Risk Measures," Working Papers hal-01367277, HAL.
    12. Maume-Deschamps Véronique & Rullière Didier & Said Khalil, 2017. "Multivariate extensions of expectiles risk measures," Dependence Modeling, De Gruyter, vol. 5(1), pages 20-44, January.
    13. Matthieu Garcin & Dominique Guegan & Bertrand Hassani, 2018. "A novel multivariate risk measure: the Kendall VaR," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01467857, HAL.
    14. 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.
    15. Torres, Raúl & Lillo, Rosa E. & Laniado, Henry, 2015. "A directional multivariate value at risk," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 111-123.
    16. Zhu, Yunzhou & Chi, Yichun & Weng, Chengguo, 2014. "Multivariate reinsurance designs for minimizing an insurer’s capital requirement," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 144-155.
    17. Christoph Frei, 2020. "A New Approach to Risk Attribution and Its Application in Credit Risk Analysis," Risks, MDPI, vol. 8(2), pages 1-13, June.
    18. Elena Bernardino & Thomas Laloë & Rémi Servien, 2015. "Estimating covariate functions associated to multivariate risks: a level set approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 497-526, July.
    19. Matthias Fischer & Thorsten Moser & Marius Pfeuffer, 2018. "A Discussion on Recent Risk Measures with Application to Credit Risk: Calculating Risk Contributions and Identifying Risk Concentrations," Risks, MDPI, vol. 6(4), pages 1-28, December.
    20. Ren Jiandong & Zitikis Ricardas, 2017. "CMPH: a multivariate phase-type aggregate loss distribution," Dependence Modeling, De Gruyter, vol. 5(1), pages 304-315, December.
    21. Shushi, Tomer & Yao, Jing, 2020. "Multivariate risk measures based on conditional expectation and systemic risk for Exponential Dispersion Models," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 178-186.

    More about this item

    Keywords

    dependence modeling; risk theory; sub-exponential distributions; copulas.; Multivariate risk indicators; optimal capital allocation;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hal:journl:hal-01171395. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.