A Coupling Proof of Convex Ordering for Compound Distributions

Jean Bérard; Nicolas Juillet

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arXiv · 1910.07218

A Coupling Proof of Convex Ordering for Compound Distributions

Jean Bérard·Nicolas Juillet

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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.

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Jean Bérard, Nicolas Juillet. 2019-10-16. A Coupling Proof of Convex Ordering for Compound Distributions. https://arxiv.org/abs/1910.07218

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