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Comonotonic Processes

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  • Elyès Jouini

    ()
    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX)

  • Clotilde Napp

    (DRM - Dauphine Recherches en Management - CNRS : UMR7088 - Université Paris Dauphine - Paris IX)

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.

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Bibliographic Info

Paper provided by HAL in its series Post-Print with number halshs-00167158.

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Date of creation: 2003
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Publication status: Published, Insurance: Mathematics and Economics, 2003, 255-265
Handle: RePEc:hal:journl:halshs-00167158

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Keywords: Comonotonicity; Comonotonic processes; Jump processes; Risk sharing schemes; Pareto optimal allocations;

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References

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  1. 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.
  2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  3. 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.
  4. Dybvig, Philip H, 1988. "Distributional Analysis of Portfolio Choice," The Journal of Business, University of Chicago Press, vol. 61(3), pages 369-93, July.
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Cited by:
  1. 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.
  2. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc0p00hch is not listed on IDEAS
  3. Puccetti, Giovanni & Scarsini, Marco, 2010. "Multivariate comonotonicity," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 291-304, January.
  4. 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.
  5. Marco Corazza & A. Malliaris & Elisa Scalco, 2010. "Nonlinear Bivariate Comovements of Asset Prices: Methodology, Tests and Applications," Computational Economics, Society for Computational Economics, vol. 35(1), pages 1-23, January.
  6. 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.

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