Generators of copulas and aggregation

The most applied class of copulas for fitting purposes is undoubtedly the class of Archimedean copulas due to their representation by means of single functions of one variable, i.e., by means of additive generators or the corresponding pseudo-inverses. In this paper, we characterize aggregation functions preserving additive generators (pseudo-inverses of additive generators) of Archimedean copulas. As a by-product, we obtain an efficient method to construct new additive generators from some given ones.