# Functional treatment of asymmetric copulas

## TL;DR

This paper refines the mathematical understanding of asymmetric copulas, introduces a topological framework for measuring asymmetry, and applies it to the asymmetric Cobb-Douglas utility model.

## Contribution

It provides a rigorous topological approach to classifying and measuring asymmetry in copulas, enhancing the theoretical foundation of the concept.

## Key findings

- Defined three classes of copulas based on asymmetry
- Established a process to order subcopulas by asymmetry degree
- Applied the framework to the asymmetric Cobb-Douglas utility model

## Abstract

The concept of asymmetric copulas is revisited and is made more precise. We give a rigorous topological argument for opportunity to define asymmetry measures defined recently by K.F Siburg [6] through exhibiting at least three ordered classes of copulas according to a suitable equivalence relation. We define a process of ordering subcopulas which makes clearer the degree of asymmetry. As illustration, we treat the asymmetric Cobb-Douglas utility model.