Bounds on Integrals with Respect to Multivariate Copulas
Optimization and Control
2016-07-01 v2 Probability
Abstract
Finding upper and lower bounds to integrals with respect to copulas is a quite prominent problem in applied probability. In their 2014 paper, Hofer and Iaco showed how particular two dimensional copulas are related to optimal solutions of the two dimensional assignment problem. Using this, they managed to approximate integrals with respect to two dimensional copulas. In this paper, we will further illuminate this connection, extend it to d-dimensional copulas and therefore generalize the method from Hofer and Iaco to arbitrary dimensions. We also provide convergence statements. As an example, we consider three dimensional dependence measures.
Cite
@article{arxiv.1606.08661,
title = {Bounds on Integrals with Respect to Multivariate Copulas},
author = {Michael Preischl},
journal= {arXiv preprint arXiv:1606.08661},
year = {2016}
}