Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 161537, 9 pages
Research Article

Bounds for Trivariate Copulas with Given Bivariate Marginals

Fabrizio Durante,1 Erich Peter Klement,1 and José Juan Quesada-Molina2

1Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, 4040 Linz, Austria
2Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain

Received 26 September 2008; Accepted 27 November 2008

Academic Editor: Paolo Ricci

Copyright © 2008 Fabrizio Durante et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We determine two constructions that, starting with two bivariate copulas, give rise to new bivariate and trivariate copulas, respectively. These constructions are used to determine pointwise upper and lower bounds for the class of all trivariate copulas with given bivariate marginals.