Distribution functions, external limits and optimal transport

作者：Iaco M R; Thonhauser S; Tichy R F^*

来源：Indagationes Mathematicae, 2015, 26(5): 823-841.

DOI：10.1016/j.indag.2015.05.003

• Distribution functions
• Optimal transport
• Linear assignment problem
• Copulas

Encouraged by the study of extremal limits for sums of the form
lim(N ->) (infinity) 1/N Sigma(N)(n=1) c(x(n), y(n))
with uniformly distributed sequences {x(n)}, {y(n)} the following extremal problem is of interest
max(gamma) integral([0,1]2) c(x, y) gamma (dx, dy),
for probability measures gamma on the unit square with uniform marginals, i.e., measures whose distribution function is a copula.
The aim of this article is to relate this problem to combinatorial optimization and to the theory of optimal transport. Using different characterizations of maximizing gamma's one can give alternative proofs of some results from the field of uniform distribution theory and beyond that treat additional questions. Finally, some applications to mathematical finance are addressed.

• 出版日期2015-12