On an upper bound of the set of copulas with a given curvilinear section

TL;DR

This paper fully characterizes when a natural upper bound of the set of copulas with a given curvilinear section is itself a copula, advancing understanding of copula bounds in this geometric context.

Contribution

It provides a complete solution to the characterization problem for the natural upper bound being a copula in the case of curvilinear sections.

Findings

Complete characterization of the upper bound as a copula for curvilinear sections

Extension of previous partial results in the literature

Clarification of conditions under which bounds are copulas

Abstract

The characterizations when two natural upper bounds of the set of copulas with a given diagonal section are copulas have been well studied in the literature. Given a curvilinear section, however, there is only a partial result concerning the characterization when a natural upper bound of the set of copulas is a copula. In this paper, we completely solve the characterization problem for this natural upper bound to be a copula in the curvilinear case.