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Stationary-excess operator and convex stochastic orders

Author

Listed:
  • Claude Lefèvre

    (ULB - Département de Mathématique [Bruxelles] - ULB - Faculté des Sciences [Bruxelles] - ULB - Université libre de Bruxelles = Free University of Brussels)

  • Stéphane Loisel

    (LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

The present paper aims to point out how the stationary-excess operator and its iterates transform the s-convex stochastic orders and the associated moment spaces. This allows us to propose a new unified method on constructing s-convex extrema for distributions that are known to be t-monotone. Both discrete and continuous cases are investigated. Several extremal distributions under monotonicity conditions are derived. They are illustrated with some applications in insurance.

Suggested Citation

  • Claude Lefèvre & Stéphane Loisel, 2010. "Stationary-excess operator and convex stochastic orders," Post-Print hal-00442047, HAL.
    • Handle: RePEc:hal:journl:hal-00442047
    Note: View the original document on HAL open archive server: https://hal.science/hal-00442047v2
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    Cited by:

    1. Anna Castañer & M. Mercè Claramunt, 2019. "Equilibrium Distributions and Discrete Schur-constant Models," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 449-459, June.
    2. repec:hal:wpaper:hal-00750562 is not listed on IDEAS
    3. Denuit, Michel & Liu, Liqun & Meyer, Jack, 2014. "A separation theorem for the weak s-convex orders," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 279-284.
    4. Manel Kacem & Claude Lefèvre & Stéphane Loisel, 2013. "Convex extrema for nonincreasing discrete distributions: effects of convexity constraints," Working Papers hal-00912942, HAL.
    5. Anna Casta~ner & M Merc`e Claramunt, 2017. "Equilibrium distributions and discrete Schur-constant models," Papers 1709.09955, arXiv.org.
    6. Anna Castañer & M Mercè Claramunt, 2017. "Equilibrium distributions and discrete Schur-constant models," Working Papers hal-01593552, HAL.
    7. Claude Lefèvre & Stéphane Loisel, 2013. "On multiply monotone distributions, continuous or discrete, with applications," Post-Print hal-00750562, HAL.

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