Joint Mixability

• 成果类型: Article
• 署名作者: Wang, Bin; Wang, Ruodu
• 署名单位: Beijing Technology & Business University; University of Waterloo
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2015.0755
• 发表日期: 2016
• 页码: 808-826
• 关键词: dependence structure; model uncertainty; aggregation; distributions; MARGINALS; risks

摘要

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.