Joint Mixability

Forthcoming in Mathematics of Operations Research

32 Pages Posted: 30 Jan 2015 Last revised: 21 Jul 2015

See all articles by Bin Wang

Bin Wang

Beijing University of Technology

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Date Written: July 14, 2015

Abstract

Many optimization problems in probabilistic combinatorics and mass transportation impose fixed marginal constraints. A natural and open question in this field is to determine all possible distributions of the sum of random variables with given marginal distributions; the notion of joint mixability is introduced to address this question. A tuple of univariate distributions is said to be jointly mixable if there exist random variables, with respective distributions, such that their sum is a constant. We obtain necessary and sufficient conditions for the joint mixability of some classes of distributions, including uniform distributions, distributions with monotone densities, distributions with unimodal-symmetric densities, and elliptical distributions with the same characteristic generator. Joint mixability is directly connected to many open questions on the optimization of convex functions and probabilistic inequalities with marginal constraints. The results obtained in this paper can be applied to find extreme scenarios on risk aggregation under model uncertainty at the level of dependence.

Keywords: joint mixability; multivariate dependence; convex optimization; optimal coupling; risk aggregation

Suggested Citation

Wang, Bin and Wang, Ruodu, Joint Mixability (July 14, 2015). Forthcoming in Mathematics of Operations Research, Available at SSRN: https://ssrn.com/abstract=2557067 or http://dx.doi.org/10.2139/ssrn.2557067

Bin Wang

Beijing University of Technology ( email )

100 Ping Le Yuan
Chaoyang District
Beijing, Beijing 100020
China

Ruodu Wang (Contact Author)

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
131
Abstract Views
883
rank
237,499
PlumX Metrics