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Stochastic Convexity of the Poisson Mixture Model

Author

Listed:
  • Michel Denuit

    (Université Catholique de Louvain)

  • Claude Lefèvre

    (Université Libre de Bruxelles)

  • Moshe Shaked

    (University of Arizona)

Abstract

This paper is devoted to the study of the compound Poisson mixture model in an actuarial framework. Using the s-convex stochastic orderings and stochastic s-convexity, several problems involving an unknown mixing parameter with given moments are examined; namely, the specification of the number of support points in a finite mixture model, and the derivation of extremal mixture distributions. The theory is enhanced with the derivation of theoretical and numerical bounds on several quantities of actuarial interest.

Suggested Citation

  • Michel Denuit & Claude Lefèvre & Moshe Shaked, 2000. "Stochastic Convexity of the Poisson Mixture Model," Methodology and Computing in Applied Probability, Springer, vol. 2(3), pages 231-254, September.
    • Handle: RePEc:spr:metcap:v:2:y:2000:i:3:d:10.1023_a:1010054211652
    DOI: 10.1023/A:1010054211652
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    References listed on IDEAS

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    1. Denuit, Michel, 1999. "The Exponential Premium Calculation Principle Revisited," ASTIN Bulletin, Cambridge University Press, vol. 29(2), pages 215-226, November.
    2. Hesselager, Ole, 1998. "Closure properties of some partial orderings under mixing," Insurance: Mathematics and Economics, Elsevier, vol. 22(2), pages 163-170, June.
    3. SIMAR, Leopold, 1976. "Maximum likelihood estimation of a compound Poisson process," LIDAM Reprints CORE 271, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Denuit, Michel, 1997. "A New Distribution of Poisson-Type for the Number of Claims," ASTIN Bulletin, Cambridge University Press, vol. 27(2), pages 229-242, November.
    5. Kaas, R. & Hesselager, O., 1995. "Ordering claim size distributions and mixed Poisson probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 17(2), pages 193-201, October.
    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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    Citations

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    Cited by:

    1. Michel M. Denuit & Mhamed Mesfioui, 2016. "Multivariate Higher-Degree Stochastic Increasing Convexity," Journal of Theoretical Probability, Springer, vol. 29(4), pages 1599-1623, December.
    2. 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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