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2020 A coupling proof of convex ordering for compound distributions
Jean Bérard, Nicolas Juillet
Electron. Commun. Probab. 25: 1-9 (2020). DOI: 10.1214/20-ECP323

Abstract

In this paper, we give an alternative proof of the fact that, when compounding a nonnegative probability distribution, convex ordering between the distributions of the number of summands implies convex ordering between the resulting compound distributions. Although this is a classical textbook result in risk theory, our proof exhibits a concrete coupling between the compound distributions being compared, using the representation of one-period discrete martingale laws as a mixture of the corresponding extremal measures.

Citation

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Jean Bérard. Nicolas Juillet. "A coupling proof of convex ordering for compound distributions." Electron. Commun. Probab. 25 1 - 9, 2020. https://doi.org/10.1214/20-ECP323

Information

Received: 25 October 2019; Accepted: 19 May 2020; Published: 2020
First available in Project Euclid: 1 July 2020

zbMATH: 1447.60048
MathSciNet: MR4125792
Digital Object Identifier: 10.1214/20-ECP323

Subjects:
Primary: 60E15, 60G50, 91B30
Secondary: 46A55, 49Q22, 60G42

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