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Impact of Dependence on Some Multivariate Risk Indicators

Author

Listed:
  • Véronique Maume-Deschamps

    (Université de Lyon, Université Claude Bernard Lyon 1)

  • Didier Rullière

    (Université de Lyon, Université Lyon 1)

  • Khalil Said

    (Université de Lyon, Université Lyon 2)

Abstract

The minimization of some multivariate risk indicators may be used as an allocation method, as proposed in Cénac et al. (Stat Risk Model 29(1):47–71, 2012). The aim of capital allocation is to choose a point in a simplex, according to a given criterion. In Maume-Deschamps et al. (2015), it is 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 also analyze 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," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 395-427, June.
    • Handle: RePEc:spr:metcap:v:19:y:2017:i:2:d:10.1007_s11009-016-9489-4
    DOI: 10.1007/s11009-016-9489-4
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    References listed on IDEAS

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    1. Areski Cousin & Elena Di Bernadino, 2013. "On Multivariate Extensions of Value-at-Risk," Working Papers hal-00638382, HAL.
    2. Cousin, Areski & Di Bernardino, Elena, 2013. "On multivariate extensions of Value-at-Risk," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 32-46.
    3. 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.
    4. Véronique Maume-Deschamps & Didier Rullière & Khalil Said, 2015. "A risk management approach to capital allocation," Working Papers hal-01163180, HAL.
    5. Elyés Jouini & Moncef Meddeb & Nizar Touzi, 2004. "Vector-valued coherent risk measures," Finance and Stochastics, Springer, vol. 8(4), pages 531-552, November.
    6. 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.
    7. 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.
    8. Mathieu Bargès & Hélène Cossette & Etienne Marceau, 2009. "TVaR-based capital allocation with copulas," Working Papers hal-00431265, HAL.
    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.
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    Cited by:

    1. Beck, Nicholas & Di Bernardino, Elena & Mailhot, Mélina, 2021. "Semi-parametric estimation of multivariate extreme expectiles," Journal of Multivariate Analysis, Elsevier, vol. 184(C).

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