Stochastic Convexity of the Poisson Mixture Model

Michel Denuit (), Claude Lefèvre () and Moshe Shaked ()
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Michel Denuit: Université Catholique de Louvain
Claude Lefèvre: Université Libre de Bruxelles
Moshe Shaked: University of Arizona

Methodology and Computing in Applied Probability, 2000, vol. 2, issue 3, 231-254

Abstract: 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.

Keywords: stochastic orders; compound Poisson; insurance; stop-loss premium; semi-variance premium; exponential premium; stochastic convexity (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1010054211652

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