On the n-Coupling Problem

By Ludger Rüschendorf, Ludger Uckelmann. 2002

63 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1e2add7d2ca21b824a047f5e9d07a3e991b27a84

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Geometry and Topology

Citations in the corpus

A fixed-point approach to barycenters in Wasserstein space (2015, methodology): “We have included a comparison to the alternative iterative procedure considered in [26], which can be summarized as follows.”
Optimal transportation with infinitely many marginals (2012, background): “xm) = ∑m i=1 ∑m j=1 |xi − xj |2 on Mi = R , the Kantorovich problem admits a unique solution which is concentrated on the graph of a function over the first marginal, generalizing Brenier’s theorem [14]; see also [22][17][26] and [27].”
On the Bures–Wasserstein distance between positive definite matrices (2017, background): “We have proved the following theorem first obtained in [1], building upon the earlier work in [22] and [31]”
Bounds for joint portfolios of dependent risks (2012, methodology): “In this case, the mixing condition is satisfied, as described in Rüschendorf and Uckelmann (2002).”
Barycenters in the Wasserstein Space (2011, background): “Let us point out here that Rüschendorf and Uckelman proved in [13] existence of a solution to (6.”
Multi-marginal optimal transport and multi-agent matching problems: uniqueness and structure of solutions (2012, background): “n certain special cases. Uniqueness and Monge solution results have been proven by Gangbo and ´Swi¸ech [17] for the quadratic surplus, b(x1,x2,...,xm) = − Xm i6= j |xi −xj|2; (1) see also [24][20][30][31]. This was generalizedby Heinich [18] to surplus functions of the form b(x1,x2,...,xm) = h( Xm i”