Department of Economics
Convex combinations of quadrant dependent copulas
It is well known that quadrant dependent (QD) random variables are also quadrant dependent in expectation (QDE). Recent literature has offered examples rigorously establishing the fact that there are QDE random variables which are not QD. The examples are based on convex combinations of specially chosen QD copulas: one negatively QD and another positively QD. In this paper we establish general results that determine when convex combinations of arbitrary QD copulas give rise to negatively or positively QD/QDE copulas. In addition to being an interesting mathematical exercise, the established results are helpful when modeling insurance and financial portfolios. © 2012 Elsevier Ltd. All rights reserved.
Convex combination, Copula, Quadrant dependence, Quadrant dependence in expectation
Source Publication Title
Applied Mathematics Letters
Egozcue, Martín, Luis Fuentes García, Wing-Keung Wong, and Ričardas Zitikis. "Convex combinations of quadrant dependent copulas." Applied Mathematics Letters 26.2 (2013): 249-251.