First-order Dominance: Stronger Characterization and a Bivariate Checking Algorithm

Troels Martin Range, Lars Peter Østerdal

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How to determine whether one distribution first-order dominates another is a fundamental problem that has many applications in economics, finance, probability theory, and statistics. Nevertheless, little is known about how to efficiently check first-order dominance for finite multivariate distributions. Utilizing that this problem can be formulated as a transportation problem with a special structure, we provide a stronger characterization of multivariate first-order dominance and develop a linear time complexity checking algorithm for the bivariate case. We illustrate the use of the checking algorithm when numerically assessing first-order dominance among continuous bivariate distributions.
Original languageEnglish
JournalMathematical Programming
Issue number1/2
Pages (from-to)193-219
Number of pages27
Publication statusPublished - Jan 2019

Bibliographical note

Published online: 2. December 2017


  • Multivariate first-order dominance
  • Usual stochastic order
  • Characterization
  • Network problem
  • Checking algorithm

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