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Pairwise counter-monotonicity

Author

Listed:
  • Jean-Gabriel Lauzier
  • Liyuan Lin
  • Ruodu Wang

Abstract

We systematically study pairwise counter-monotonicity, an extremal notion of negative dependence. A stochastic representation and an invariance property are established for this dependence structure. We show that pairwise counter-monotonicity implies negative association, and it is equivalent to joint mix dependence if both are possible for the same marginal distributions. We find an intimate connection between pairwise counter-monotonicity and risk sharing problems for quantile agents. This result highlights the importance of this extremal negative dependence structure in optimal allocations for agents who are not risk averse in the classic sense.

Suggested Citation

  • Jean-Gabriel Lauzier & Liyuan Lin & Ruodu Wang, 2023. "Pairwise counter-monotonicity," Papers 2302.11701, arXiv.org, revised May 2023.
    • Handle: RePEc:arx:papers:2302.11701
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    Cited by:

    1. Han, Xia & Lin, Liyuan & Wang, Ruodu, 2023. "Diversification quotients based on VaR and ES," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 185-197.
    2. Peng Liu & Andreas Tsanakas & Yunran Wei, 2024. "Risk sharing with Lambda value at risk under heterogeneous beliefs," Papers 2408.03147, arXiv.org, revised Sep 2024.
    3. Jean-Gabriel Lauzier & Liyuan Lin & Ruodu Wang, 2024. "Optimal sharing, equilibria, and welfare without risk aversion," Papers 2401.03328, arXiv.org, revised Dec 2024.

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