Discrete imprecise copulas and alternating sign matrices

Abstract

In this paper, we study discrete quasi-copulas and discrete imprecise copulas of minimal range, which naturally correspond to alternating sign matrices. We show that this family is invariant under all defect transformations on quasi-copulas and give a constructive proof demonstrating that discrete imprecise copulas of minimal range do not, in general, avoid sure loss. In contrast, we show that discrete imprecise copulas of minimal range that correspond to dense alternating sign matrices are always coherent, and hence avoid sure loss.