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Stationary-excess operator and convex stochastic orders

Author

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  • Claude Lefèvre

    (ULB - Département de Mathématique [Bruxelles] - ULB - Faculté des Sciences [Bruxelles] - ULB - Université libre de Bruxelles)

  • Stéphane Loisel

    (SAF - 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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    References listed on IDEAS

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    1. Denuit, Michel & Lefevre, Claude & Mesfioui, M'hamed, 1999. "On s-convex stochastic extrema for arithmetic risks," Insurance: Mathematics and Economics, Elsevier, vol. 25(2), pages 143-155, November.
    2. Cheng, Yu & Pai, Jeffrey S., 2003. "On the nth stop-loss transform order of ruin probability," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 51-60, February.
    3. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    4. Jansen, K. & Haezendonck, J. & Goovaerts, M. J., 1986. "Upper bounds on stop-loss premiums in case of known moments up to the fourth order," Insurance: Mathematics and Economics, Elsevier, vol. 5(4), pages 315-334, October.
    5. Denuit, Michel & Lefevre, Claude, 1997. "Some new classes of stochastic order relations among arithmetic random variables, with applications in actuarial sciences," Insurance: Mathematics and Economics, Elsevier, vol. 20(3), pages 197-213, October.
    6. Peter C. Fishburn & Irving H. Lavalle, 1995. "Stochastic Dominance on Unidimensional Grids," Mathematics of Operations Research, INFORMS, vol. 20(3), pages 513-525, August.
    7. Denuit, Michel & Vylder, Etienne De & Lefevre, Claude, 1999. "Extremal generators and extremal distributions for the continuous s-convex stochastic orderings," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 201-217, May.
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    Cited by:

    1. Anna Casta~ner & M Merc`e Claramunt, 2017. "Equilibrium distributions and discrete Schur-constant models," Papers 1709.09955, arXiv.org.
    2. 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.
    3. 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.
    4. repec:hal:wpaper:hal-00750562 is not listed on IDEAS
    5. Anna Castañer & M Mercè Claramunt, 2017. "Equilibrium distributions and discrete Schur-constant models," Working Papers hal-01593552, HAL.
    6. Claude Lefèvre & Stéphane Loisel, 2013. "On multiply monotone distributions, continuous or discrete, with applications," Post-Print hal-00750562, HAL.
    7. Manel Kacem & Claude Lefèvre & Stéphane Loisel, 2013. "Convex extrema for nonincreasing discrete distributions: effects of convexity constraints," Working Papers hal-00912942, HAL.

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