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Impact of dependence on some multivariate risk indicators

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  • 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
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    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.
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    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).

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    Keywords

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