A Coupling Proof of Convex Ordering for Compound Distributions
Probability
2019-10-17 v1
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.
Cite
@article{arxiv.1910.07218,
title = {A Coupling Proof of Convex Ordering for Compound Distributions},
author = {Jean Bérard and Nicolas Juillet},
journal= {arXiv preprint arXiv:1910.07218},
year = {2019}
}