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Comonotonic processes

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  • Jouini, Elyes
  • Napp, Clotilde

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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Suggested Citation

  • Jouini, Elyes & Napp, Clotilde, 2003. "Comonotonic processes," Insurance: Mathematics and Economics, Elsevier, vol. 32(2), pages 255-265, April.
    • Handle: RePEc:eee:insuma:v:32:y:2003:i:2:p:255-265
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    References listed on IDEAS

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    1. Dybvig, Philip H, 1988. "Distributional Analysis of Portfolio Choice," The Journal of Business, University of Chicago Press, vol. 61(3), pages 369-393, July.
    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. 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.
    5. 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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    Citations

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    Cited by:

    1. Guillaume Carlier & Rose-Anne Dana & Alfred Galichon, 2012. "Pareto efficiency for the concave order and multivariate comonotonicity," SciencePo Working papers Main hal-01053549, HAL.
    2. 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".
    3. Sebastian Sitarz, 2009. "Pareto optimal allocations and dynamic programming," Annals of Operations Research, Springer, vol. 172(1), pages 203-219, November.
    4. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc0p00hch is not listed on IDEAS
    5. Guillaume Carlier & Rose-Anne Dana & Alfred Galichon, 2012. "Pareto efficiency for the concave order and multivariate comonotonicity," SciencePo Working papers hal-01053549, HAL.
    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.
    7. repec:dau:papers:123456789/9713 is not listed on IDEAS
    8. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc0p00hch is not listed on IDEAS
    9. 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.
    10. repec:spo:wpmain:info:hdl:2441/5rkqqmvrn4tl22s9mc0p00hch is not listed on IDEAS
    11. 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.
    12. 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.
    13. 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.
    14. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc0p00hch is not listed on IDEAS
    15. Puccetti, Giovanni & Scarsini, Marco, 2010. "Multivariate comonotonicity," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 291-304, January.

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