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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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Bibliographic Info

Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 32 (2003)
Issue (Month): 2 (April)
Pages: 255-265

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Handle: RePEc:eee:insuma:v:32:y:2003:i:2:p:255-265

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Web page: http://www.elsevier.com/locate/inca/505554

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References

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  1. Philip H. Dybvig, 1987. "Distributional Analysis of Portfolio Choice," Cowles Foundation Discussion Papers 827R, Cowles Foundation for Research in Economics, Yale University, revised Jan 1988.
  2. 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.
  3. 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.
  4. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
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Cited by:
  1. Galichon, Alfred & Dana, Rose-Anne & Carlier, Guillaume, 2012. "Pareto efficiency for the concave order and multivariate comonotonicity," Economics Papers from University Paris Dauphine 123456789/9713, Paris Dauphine University.
  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. 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.
  5. 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.
  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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