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Finding upper and lower bounds to integrals with respect to copulas is aquite prominent problem in applied probability. In their 2014 paper, Hofer andIaco showed how particular two dimensional copulas are related to optimalsolutions of the two dimensional assignment problem. Using this, they managedto approximate integrals with respect to two dimensional copulas. In thispaper, we will further illuminate this connection, extend it to d-dimensionalcopulas and therefore generalize the method from Hofer and Iaco to arbitrarydimensions. We also provide convergence statements. As an example, we considerthree dimensional dependence measures.

Bounds on Integrals with Respect to Multivariate Copulas