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Some Remarks on the Supermodular Order

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  • Müller, Alfred
  • Scarsini, Marco

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

  • Müller, Alfred & Scarsini, Marco, 2000. "Some Remarks on the Supermodular Order," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 107-119, April.
    • Handle: RePEc:eee:jmvana:v:73:y:2000:i:1:p:107-119
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    References listed on IDEAS

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    1. Block, Henry W. & Sampson, Allan R., 1988. "Conditionally ordered distributions," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 91-104, October.
    2. Muller, Alfred, 1997. "Stop-loss order for portfolios of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 219-223, December.
    3. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
    4. 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.
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