Comonotonicity, orthant convex order and sums of random variables

Mesfioui, Mhamed;Denuit, Michel
(2015) Statistics & Probability Letters — Vol. 96, p. 356-364 (2015)

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Abstract
This paper extends a useful property of the increasing convex order to the multivariate orthant convex order. Specifically, it is shown that vectors of sums of comonotonic random variables dominate in the orthant convex order vectors of sums of random variables that are smaller in the increasing convex sense, whatever their dependence structure. This result is then used to derive orthant convex order bounds on random vectors of sums of random variables. Extensions to vectors of compound sums are also discussed.
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Mesfioui, M., & Denuit, M. (2015). Comonotonicity, orthant convex order and sums of random variables. Statistics & Probability Letters, 96, 356-364. https://doi.org/10.1016/j.spl.2014.10.004 (Original work published 2015)