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Characterizing mutual exclusivity as the strongest negative multivariate dependence structure

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  • Cheung, Ka Chun
  • Lo, Ambrose

Abstract

Mutual exclusivity is an extreme negative dependence structure that was first proposed and studied in Dhaene and Denuit (1999) in the context of insurance risks. In this article, we revisit this notion and present versatile characterizations of mutually exclusive random vectors via their pairwise counter-monotonic behaviour, minimal convex sum property, distributional representation and the characteristic function of the sum of their components. These characterizations highlight the role of mutual exclusivity in generalizing counter-monotonicity as the strongest negative dependence structure in a multi-dimensional setting.

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  • Cheung, Ka Chun & Lo, Ambrose, 2014. "Characterizing mutual exclusivity as the strongest negative multivariate dependence structure," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 180-190.
    • Handle: RePEc:eee:insuma:v:55:y:2014:i:c:p:180-190
    DOI: 10.1016/j.insmatheco.2014.01.001
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    1. Dhaene, Jan & Goovaerts, Marc J., 1996. "Dependency of Risks and Stop-Loss Order1," ASTIN Bulletin, Cambridge University Press, vol. 26(2), pages 201-212, November.
    2. Cheung, Ka Chun, 2008. "Characterization of comonotonicity using convex order," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 403-406, December.
    3. Ruodu Wang & Liang Peng & Jingping Yang, 2013. "Bounds for the sum of dependent risks and worst Value-at-Risk with monotone marginal densities," Finance and Stochastics, Springer, vol. 17(2), pages 395-417, April.
    4. Cheung, Ka Chun, 2010. "Characterizing a comonotonic random vector by the distribution of the sum of its components," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 130-136, October.
    5. Cheung, Ka Chun & Lo, Ambrose, 2013. "General lower bounds on convex functionals of aggregate sums," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 884-896.
    6. Rob Kaas & Marc Goovaerts & Jan Dhaene & Michel Denuit, 2008. "Modern Actuarial Risk Theory," Springer Books, Springer, edition 2, number 978-3-540-70998-5, September.
    7. Dhaene, Jan & Denuit, Michel, 1999. "The safest dependence structure among risks," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 11-21, September.
    8. Wang, Bin & Wang, Ruodu, 2011. "The complete mixability and convex minimization problems with monotone marginal densities," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1344-1360, November.
    9. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    10. Cheung, Ka Chun & Lo, Ambrose, 2013. "Characterizations of counter-monotonicity and upper comonotonicity by (tail) convex order," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 334-342.
    11. Cheung, Ka Chun & Dhaene, Jan & Lo, Ambrose & Tang, Qihe, 2014. "Reducing risk by merging counter-monotonic risks," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 58-65.
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    Cited by:

    1. 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.
    2. Jae Youn Ahn & Sebastian Fuchs, 2020. "On Minimal Copulas under the Concordance Order," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 762-780, March.
    3. Chuancun Yin & Dan Zhu, 2016. "Sharp convex bounds on the aggregate sums--An alternative proof," Papers 1603.05373, arXiv.org, revised May 2016.
    4. Jan L. M. Dhaene & Moshe A. Milevsky, 2024. "Egalitarian pooling and sharing of longevity risk', a.k.a. 'The many ways to skin a tontine cat," Papers 2402.00855, arXiv.org.
    5. Lee, Woojoo & Ahn, Jae Youn, 2014. "On the multidimensional extension of countermonotonicity and its applications," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 68-79.
    6. Jae Youn Ahn, 2015. "Negative Dependence Concept in Copulas and the Marginal Free Herd Behavior Index," Papers 1503.03180, arXiv.org.
    7. Takaaki Koike & Liyuan Lin & Ruodu Wang, 2022. "Joint mixability and notions of negative dependence," Papers 2204.11438, arXiv.org, revised Jan 2024.
    8. Jean-Gabriel Lauzier & Liyuan Lin & Ruodu Wang, 2023. "Pairwise counter-monotonicity," Papers 2302.11701, arXiv.org, revised May 2023.
    9. Chaoubi, Ihsan & Cossette, Hélène & Gadoury, Simon-Pierre & Marceau, Etienne, 2020. "On sums of two counter-monotonic risks," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 47-60.
    10. Lauzier, Jean-Gabriel & Lin, Liyuan & Wang, Ruodu, 2023. "Pairwise counter-monotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 279-287.
    11. Chuancun Yin & Dan Zhu, 2016. "Sharp Convex Bounds on the Aggregate Sums–An Alternative Proof," Risks, MDPI, vol. 4(4), pages 1-8, September.
    12. Jean-Gabriel Lauzier & Liyuan Lin & Ruodu Wang, 2024. "Negatively dependent optimal risk sharing," Papers 2401.03328, arXiv.org.

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