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Reducing risk by merging counter-monotonic risks

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  • Cheung, Ka Chun
  • Dhaene, Jan
  • Lo, Ambrose
  • Tang, Qihe

Abstract

In this article, we show that some important implications concerning comonotonic couples and corresponding convex order relations for their sums cannot be translated to counter-monotonicity in general. In a financial context, it amounts to saying that merging counter-monotonic positions does not necessarily reduce the overall level of risk. We propose a simple necessary and sufficient condition for such a merge to be effective. Natural interpretations and various characterizations of this condition are given. As applications, we develop cancelation laws for convex order and identify desirable structural properties of insurance indemnities that make an insurance contract universally marketable, in the sense that it is appealing to both the policyholder and the insurer.

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  • 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.
    • Handle: RePEc:eee:insuma:v:54:y:2014:i:c:p:58-65
    DOI: 10.1016/j.insmatheco.2013.10.014
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    References listed on IDEAS

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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. Aouani, Zaier & Chateauneuf, Alain & Ventura, Caroline, 2021. "Propensity for hedging and ambiguity aversion," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    3. Jean-Gabriel Lauzier & Liyuan Lin & Ruodu Wang, 2023. "Pairwise counter-monotonicity," Papers 2302.11701, arXiv.org, revised May 2023.
    4. Feng, Runhuan & Liu, Ming & Zhang, Ning, 2024. "A unified theory of decentralized insurance," Insurance: Mathematics and Economics, Elsevier, vol. 119(C), pages 157-178.
    5. Mario Ghossoub & Qinghua Ren & Ruodu Wang, 2024. "Counter-monotonic Risk Sharing with Heterogeneous Distortion Risk Measures," Papers 2412.00655, arXiv.org.
    6. He, Junnan & Tang, Qihe & Zhang, Huan, 2016. "Risk reducers in convex order," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 80-88.
    7. Yuanying Guan & Muqiao Huang & Ruodu Wang, 2024. "A new characterization of second-order stochastic dominance," Papers 2402.13355, arXiv.org, revised Sep 2024.
    8. 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.
    9. Chunle Huang, 2025. "Distortion risk measures of sums of two counter-monotonic risks," Papers 2503.05256, arXiv.org.
    10. Samuel Solgon Santos & Marcelo Brutti Righi & Eduardo de Oliveira Horta, 2022. "The limitations of comonotonic additive risk measures: a literature review," Papers 2212.13864, arXiv.org, revised Jan 2024.
    11. Guan, Yuanying & Huang, Muqiao & Wang, Ruodu, 2024. "A new characterization of second-order stochastic dominance," Insurance: Mathematics and Economics, Elsevier, vol. 119(C), pages 261-267.
    12. Bernard, Carole & Liu, Fangda & Vanduffel, Steven, 2020. "Optimal insurance in the presence of multiple policyholders," Journal of Economic Behavior & Organization, Elsevier, vol. 180(C), pages 638-656.
    13. Ghossoub, Mario, 2019. "Optimal insurance under rank-dependent expected utility," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 51-66.
    14. Lauzier, Jean-Gabriel & Lin, Liyuan & Wang, Ruodu, 2023. "Pairwise counter-monotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 279-287.
    15. 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.

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