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Conditional Comonotonicity

Author

Listed:
  • Clotilde Napp

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique)

  • Elyès Jouini

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract
In this paper we propose a generalization of the comonotonicity notion by introducing and exploring the concept of conditional comonotonicity. We characterize this notion and we show on examples that conditional comonotonicity is the natural extension of the concept of comonotonicity to dynamic settings.

Suggested Citation

  • Clotilde Napp & Elyès Jouini, 2005. "Conditional Comonotonicity," Post-Print halshs-00151516, HAL.
    • Handle: RePEc:hal:journl:halshs-00151516
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00151516
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    References listed on IDEAS

    as
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    7. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    8. Wang, Shaun & Dhaene, Jan, 1998. "Comonotonicity, correlation order and premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 235-242, July.
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    Cited by:

    1. Takao Asano & Hiroyuki Kojima, 2019. "Consequentialism and dynamic consistency in updating ambiguous beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(1), pages 223-250, July.
    2. Guillaume Carlier & Rose-Anne Dana & Alfred Galichon, 2012. "Pareto efficiency for the concave order and multivariate comonotonicity," SciencePo Working papers Main hal-01053549, HAL.
    3. Graham, Bryan S. & Hahn, Jinyong & Poirier, Alexandre & Powell, James L., 2018. "A quantile correlated random coefficients panel data model," Journal of Econometrics, Elsevier, vol. 206(2), pages 305-335.
    4. Cheung, Ka Chun, 2008. "Improved convex upper bound via conditional comonotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 651-655, April.
    5. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc0p00hch is not listed on IDEAS
    6. Guillaume Carlier & Rose-Anne Dana & Alfred Galichon, 2012. "Pareto efficiency for the concave order and multivariate comonotonicity," SciencePo Working papers hal-01053549, HAL.
    7. Marc Rieger, 2011. "Co-monotonicity of optimal investments and the design of structured financial products," Finance and Stochastics, Springer, vol. 15(1), pages 27-55, January.
    8. repec:dau:papers:123456789/9713 is not listed on IDEAS
    9. S. Hochrainer-Stigler & N. Lugeri & M. Radziejewski, 2014. "Up-scaling of impact dependent loss distributions: a hybrid convolution approach for flood risk in Europe," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 70(2), pages 1437-1451, January.
    10. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc0p00hch is not listed on IDEAS
    11. Wu, Xianyi & Zhou, Xian, 2006. "A new characterization of distortion premiums via countable additivity for comonotonic risks," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 324-334, April.
    12. Santos, Samuel S. & Moresco, Marlon R. & Righi, Marcelo B. & Horta, Eduardo, 2024. "A note on the induction of comonotonic additive risk measures from acceptance sets," Statistics & Probability Letters, Elsevier, vol. 208(C).
    13. repec:spo:wpmain:info:hdl:2441/5rkqqmvrn4tl22s9mc0p00hch is not listed on IDEAS
    14. Zang, Xin & Jiang, Fan & Xia, Chenxi & Yang, Jingping, 2024. "Random distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 51-73.
    15. Cheung, Ka Chun, 2009. "Applications of conditional comonotonicity to some optimization problems," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 89-93, August.
    16. Carlier, G. & Dana, R.-A. & Galichon, A., 2012. "Pareto efficiency for the concave order and multivariate comonotonicity," Journal of Economic Theory, Elsevier, vol. 147(1), pages 207-229.
    17. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc0p00hch is not listed on IDEAS
    18. Cheung, K.C. & Rong, Yian & Yam, S.C.P., 2014. "Borch’s Theorem from the perspective of comonotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 144-151.
    19. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
    20. Puccetti, Giovanni & Scarsini, Marco, 2010. "Multivariate comonotonicity," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 291-304, January.
    21. Tahir Choulli & Christophe Stricker & Jia Li, 2007. "Minimal Hellinger martingale measures of order q," Finance and Stochastics, Springer, vol. 11(3), pages 399-427, July.

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    Keywords

    comonotonicity; dynamic comonotonicity;

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