New copulas and their applications to symmetrizations of bivariate copulas

TL;DR

This paper introduces new copulas derived from perturbation theory to facilitate symmetrization of asymmetric copulas, explores properties of the symmetrized versions, and examines families with prescribed symmetrizations, including topological aspects of symmetric copulas.

Contribution

It presents novel copulas based on perturbation theory and analyzes their properties and applications in symmetrization, including topological insights into symmetric copulas.

Findings

New copulas based on perturbation theory are introduced.

Properties of symmetrized copulas are characterized.

The topological structure of symmetric copulas is studied.

Abstract

New copulas, based on perturbation theory, are introduced to clarify a \emph{symmetrization} procedure for asymmetric copulas. We give also some properties of the \emph{symmetrized} copula. Finally, we examine families of copulas with a prescribed symmetrized one. By the way, we study topologically, the set of all symmetric copulas and give some of its classical and new properties.