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Some new classes of stochastic order relations among arithmetic random variables, with applications in actuarial sciences

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  • Denuit, Michel
  • Lefevre, Claude

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  • 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.
    • Handle: RePEc:eee:insuma:v:20:y:1997:i:3:p:197-213
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    1. Kaas, R. & Van Heerwaarden, A. E., 1990. "Ordering of risks and ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 9(2-3), pages 177-178, September.
    2. Fishburn, Peter C., 1976. "Continua of stochastic dominance relations for bounded probability distributions," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 295-311, December.
    3. Hesselager, Ole, 1995. "Order relations for some distributions," Insurance: Mathematics and Economics, Elsevier, vol. 16(2), pages 129-134, May.
    4. Fishburn, Peter C., 1980. "Continua of stochastic dominance relations for unbounded probability distributions," Journal of Mathematical Economics, Elsevier, vol. 7(3), pages 271-285, December.
    5. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    6. Steenackers, A. & Goovaerts, M. J., 1991. "Bounds on stop-loss premiums and ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 10(2), pages 153-159, July.
    7. Gerber, Hans U., 1988. "Mathematical Fun with the Compound Binomial Process," ASTIN Bulletin, Cambridge University Press, vol. 18(2), pages 161-168, November.
    8. Goovaerts, M. J. & De Vylder, F. & Haezendonck, J., 1982. "Ordering of risks: a review," Insurance: Mathematics and Economics, Elsevier, vol. 1(2), pages 131-161, April.
    9. Panjer, Harry H., 1981. "Recursive Evaluation of a Family of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 22-26, June.
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    Cited by:

    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. Michel M. Denuit & Mhamed Mesfioui, 2016. "Multivariate Higher-Degree Stochastic Increasing Convexity," Journal of Theoretical Probability, Springer, vol. 29(4), pages 1599-1623, December.
    3. Courtois, Cindy & Denuit, Michel, 2008. "Convex bounds on multiplicative processes, with applications to pricing in incomplete markets," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 95-100, February.
    4. Calabrese, Raffaella, 2013. "Uniform correlation structure and convex stochastic ordering in the Pólya urn scheme," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 272-277.
    5. Lefèvre, Claude & Loisel, Stéphane, 2010. "Stationary-excess operator and convex stochastic orders," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 64-75, August.
    6. Denuit, Michel & Rey, Béatrice, 2013. "Another look at risk apportionment," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 335-343.
    7. Denuit, Michel & Lefevre, Claude & Utev, Sergey, 2002. "Measuring the impact of dependence between claims occurrences," Insurance: Mathematics and Economics, Elsevier, vol. 30(1), pages 1-19, February.
    8. Denuit, Michel & Vermandele, Catherine, 1998. "Optimal reinsurance and stop-loss order," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 229-233, July.
    9. Denuit, Michel & Lefevre, Claude & Mesfioui, M'hamed, 1999. "A class of bivariate stochastic orderings, with applications in actuarial sciences," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 31-50, March.
    10. MERCIER, Sophie & CASTRO, I.T., 2019. "Stochastic comparisons of imperfect maintenance models for a gamma deteriorating system," European Journal of Operational Research, Elsevier, vol. 273(1), pages 237-248.
    11. repec:hal:wpaper:hal-00750562 is not listed on IDEAS
    12. Michel Denuit & Claude Lefèvre & Sergey Utev, 1999. "Stochastic Orderings of Convex/Concave-Type on an Arbitrary Grid," Mathematics of Operations Research, INFORMS, vol. 24(4), pages 835-846, November.
    13. Denuit, Michel, 2001. "Laplace transform ordering of actuarial quantities," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 83-102, August.
    14. Cindy Courtois & Michel Denuit, 2009. "Moment Bounds on Discrete Expected Stop-Loss Transforms, with Applications," Methodology and Computing in Applied Probability, Springer, vol. 11(3), pages 307-338, September.
    15. 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.
    16. Denuit, Michel & Van Bellegem, Sébastien, 2001. "On the stop-loss and total variation distances between random sums," Statistics & Probability Letters, Elsevier, vol. 53(2), pages 153-165, June.
    17. Claude Lefèvre & Stéphane Loisel, 2013. "On multiply monotone distributions, continuous or discrete, with applications," Post-Print hal-00750562, HAL.
    18. Denuit, Michel, 2000. "Time stochastic s-convexity of claim processes," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 203-211, May.
    19. Werner Hürlimann, 2005. "Improved Analytical Bounds for Gambler’s Ruin Probabilities," Methodology and Computing in Applied Probability, Springer, vol. 7(1), pages 79-95, March.
    20. Manel Kacem & Claude Lefèvre & Stéphane Loisel, 2013. "Convex extrema for nonincreasing discrete distributions: effects of convexity constraints," Working Papers hal-00912942, HAL.
    21. Denuit, Michel & Mesfioui, Mhamed, 2013. "Multivariate higher-degree stochastic increasing convexity," LIDAM Discussion Papers ISBA 2013016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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