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Comonotonic Processes

Author

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  • 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)

  • 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] - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

Abstract

We consider in this paper two Markovian processes X and Y, solutions of a stochastic differential equation with jumps, that are comonotonic, i.e., that are such that for all t, almost surely, X_{t} is greater in one state of the world than in another if and only if the same is true for Y_{t}. This notion of comonotonicity can be of great use for finance, insurance and actuarial issues. We show here that the assumption of comonotonicity imposes strong constraints on the coefficients of the diffusion part of X and Y.

Suggested Citation

  • Elyès Jouini & Clotilde Napp, 2003. "Comonotonic Processes," Post-Print halshs-00167158, HAL.
    • Handle: RePEc:hal:journl:halshs-00167158
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00167158v1
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    1. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc0p00hch is not listed on IDEAS
    2. repec:spo:wpmain:info:hdl:2441/5rkqqmvrn4tl22s9mc0p00hch is not listed on IDEAS
    3. Marco Corazza & A. Malliaris & Elisa Scalco, 2010. "Nonlinear Bivariate Comovements of Asset Prices: Methodology, Tests and Applications," Computational Economics, Springer;Society for Computational Economics, vol. 35(1), pages 1-23, January.
    4. Liebrich, Felix-Benedikt & Svindland, Gregor, 2019. "Efficient allocations under law-invariance: A unifying approach," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 28-45.
    5. 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.
    6. Puccetti, Giovanni & Scarsini, Marco, 2010. "Multivariate comonotonicity," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 291-304, January.
    7. Guillaume Carlier & Rose-Anne Dana & Alfred Galichon, 2012. "Pareto efficiency for the concave order and multivariate comonotonicity," Sciences Po Economics Publications (main) hal-01053549, HAL.
    8. Marco Corazza & Elisa Scalco, 2015. "Verifying the R�nyi dependence axioms for a non-linear bivariate comovement index," Working Papers 2015:11, Department of Economics, University of Venice "Ca' Foscari".
    9. Sebastian Sitarz, 2009. "Pareto optimal allocations and dynamic programming," Annals of Operations Research, Springer, vol. 172(1), pages 203-219, November.
    10. Guillaume Carlier & Rose-Anne Dana & Alfred Galichon, 2012. "Pareto efficiency for the concave order and multivariate comonotonicity," SciencePo Working papers hal-01053549, HAL.
    11. 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.
    12. repec:dau:papers:123456789/9713 is not listed on IDEAS
    13. 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.

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