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Tail mutual exclusivity and Tail-VaR lower bounds

Author

Listed:
  • Ka Chun Cheung
  • Michel Denuit
  • Jan Dhaene

Abstract

In this paper, we extend the concept of mutual exclusivity proposed by [Dhaene, J. & Denuit, M. (1999). The safest dependence structure among risks. Insurance: Mathematics and Economics 25, 11–21] to its tail counterpart and baptize this new dependency structure as tail mutual exclusivity. Probability levels are first specified for each component of the random vector. Under this dependency structure, at most one exceedance over the corresponding Value-at-Risks (VaRs) is possible, the other components being zero in such a case. No condition is imposed when all components stay below the VaRs. Several properties of this new negative dependence concept are derived. We show that this dependence structure gives rise to the smallest value of Tail-VaR (TVaR) of a sum of risks within a given Fréchet space, provided that the probability level of the TVaR is close enough to one.

Suggested Citation

  • Ka Chun Cheung & Michel Denuit & Jan Dhaene, 2017. "Tail mutual exclusivity and Tail-VaR lower bounds," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2017(1), pages 88-104, January.
    • Handle: RePEc:taf:sactxx:v:2017:y:2017:i:1:p:88-104
    DOI: 10.1080/03461238.2015.1084945
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    Cited by:

    1. Jean-Gabriel Lauzier & Liyuan Lin & Ruodu Wang, 2023. "Pairwise counter-monotonicity," Papers 2302.11701, arXiv.org, revised May 2023.
    2. Lauzier, Jean-Gabriel & Lin, Liyuan & Wang, Ruodu, 2023. "Pairwise counter-monotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 279-287.
    3. Jae Youn Ahn, 2015. "Negative Dependence Concept in Copulas and the Marginal Free Herd Behavior Index," Papers 1503.03180, arXiv.org.
    4. Hanbali, Hamza & Dhaene, Jan & Linders, Daniël, 2022. "Dependence bounds for the difference of stop-loss payoffs on the difference of two random variables," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 22-37.

    More about this item

    JEL classification:

    • G19 - Financial Economics - - General Financial Markets - - - Other
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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