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Some remarks on the supermodular order

Author

Listed:
  • Marco Scarsini

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique, Dipartimento di Scienze Economiche e Aziendali - LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma])

  • Alfred Muller

Abstract

In this paper we solve two open problems posed by Joe (1997) concerning the supermodular order. First we give an example which shows that the supermodular order is strictly stronger than the concordance order for dimension d=3. Second we show that the supermodular order fulfils all desirable properties of a multivariate positive dependence order. We especially prove the non-trivial fact that it is closed with respect to weak convergence. This is applied to give a complete characterization of the supermodular order for multivariate normal distributions.

Suggested Citation

  • Marco Scarsini & Alfred Muller, 2000. "Some remarks on the supermodular order," Post-Print hal-00540239, HAL.
    • Handle: RePEc:hal:journl:hal-00540239
    DOI: 10.1006/jmva.1999.1867
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    References listed on IDEAS

    as
    1. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
    2. Block, Henry W. & Sampson, Allan R., 1988. "Conditionally ordered distributions," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 91-104, October.
    3. Shaked, Moshe & Shanthikumar, J. George, 1997. "Supermodular Stochastic Orders and Positive Dependence of Random Vectors," Journal of Multivariate Analysis, Elsevier, vol. 61(1), pages 86-101, April.
    4. Muller, Alfred, 1997. "Stop-loss order for portfolios of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 219-223, December.
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