Freedom in constructing quasi-copulas vs. copulas

TL;DR

This paper explores the flexibility in constructing quasi-copulas compared to copulas, introducing three new methods based on recent theoretical advancements to better understand their structure and properties.

Contribution

It presents three novel construction methods for quasi-copulas, extending existing theories and providing new tools for their analysis and application.

Findings

Three construction methods for quasi-copulas are introduced.

Representation of multivariate quasi-copulas via infima and suprema of copulas.

Extension of shuffles of min to quasi-copulas.

Abstract

The main goal of this paper is to study the extent of freedom one has in constructing quasi-copulas vs. copulas. Specifically, it exhibits three construction methods for quasi-copulas based on recent developments: a representation of multivariate quasi-copulas by means of infima and suprema of copulas, an extension of a classical result on shuffles of min to the setting of quasi-copulas, and a construction method for quasi-copulas obeying a given signed mass pattern on a patch.