Extending sub-quasi-copulas

The main result of this paper is a method that gives all possible quasi-copulas that extend a given sub-quasi-copula to the whole domain, i.e., unit square [0, 1] x [0, 1]. It is known that extending quasi-copulas is a deeper challenge than extending copulas, so we need to develop new techniques to do that. Perhaps surprisingly, our method is at the same time elementary and universal - two seemingly contradicting properties that none of the known methods for extending copulas seem to possesses. We also give a construction of two quasi-copulas that unveil an interesting counterexample in imprecise probability theory. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

The paper presents a method that gives all possible quasi-copulas that extend a given sub-quasi-copula to the whole domain, as well as a construction of two quasi-copulas that unveil an interesting counterexample in imprecise probability theory.