Discrete Imprecise Copulas

TL;DR

This paper explores discrete imprecise copulas linked to Alternating Sign Matrices, introducing construction methods for dual pairs and self-dual copulas, ensuring coherence and avoiding sure loss.

Contribution

It presents new construction techniques for dual pairs and self-dual imprecise copulas in the discrete setting, connecting them with Alternating Sign Matrices.

Findings

Constructed dual pairs are coherent.

Constructed copulas avoid sure loss.

Methods for obtaining self-dual copulas are demonstrated.

Abstract

In this paper, we study discrete quasi-copulas associated with imprecise copulas. We focus on discrete imprecise copulas that are in correspondence with the Alternating Sign Matrices and provide some construction techniques of dual pairs. Additionally, we show how to obtain (full-domain) self-dual imprecise copulas through patchwork techniques. We further investigate the properties of the constructed dual pairs and prove that they are coherent and avoid sure loss.