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Stationary-excess operator and convex stochastic orders

Listed author(s):
  • Claude Lefèvre


    (ULB - Département de Mathématique [Bruxelles] - ULB - Université Libre de Bruxelles [Bruxelles])

  • Stéphane Loisel


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

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.

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Paper provided by HAL in its series Post-Print with number hal-00442047.

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Date of creation: 2010
Publication status: Published in Insurance Mathematics and Economics, 2010, 47, pp.64-75
Handle: RePEc:hal:journl:hal-00442047
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  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
  6. 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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