Methodology and Computing in Applied Probability

, Volume 18, Issue 3, pp 653–674 | Cite as

Vector-Valued Tail Value-at-Risk and Capital Allocation

  • Hélène Cossette
  • Mélina Mailhot
  • Étienne Marceau
  • Mhamed Mesfioui


Enterprise risk management, actuarial science or finance are practice areas in which risk measures are important to evaluate for heterogeneous classes of homogeneous risks. We present new measures: bivariate lower and upper orthant Tail Value-at-Risk. They are based on bivariate lower and upper orthant Value-at-Risk, introduced in Cossette et al. (Insurance: Math Econ 50(2):247–256, 2012). Many properties and applications are derived. Notably, they are shown to be positive homogeneous, invariant under translation and subadditive in distribution. Capital allocation criteria are suggested. Moreover, results on the sum of random pairs are presented, allowing to use a more accurate model for dependent classes of homogeneous risks.


Bivariate Tail Value-at-Risk Multivariate risk measures Capital allocation Copulas Bounds 

Mathematics Subject Classification (2010)

62P05 91B30 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Hélène Cossette
    • 1
  • Mélina Mailhot
    • 2
  • Étienne Marceau
    • 1
  • Mhamed Mesfioui
    • 3
  1. 1.École d’ActuariatUniversité LavalQuebec CityCanada
  2. 2.Department of Mathematics and StatisticsConcordia UniversityMontréalCanada
  3. 3.Département de Mathématiques et InformatiqueUniversité du Québec à Trois-RiviàresTrois-RiviéresCanada

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