Lorenz-Generated Bivariate Archimedean Copulas

22 Pages Posted: 7 Jun 2019 Last revised: 26 Jun 2020

See all articles by Andrea Fontanari

Andrea Fontanari

Delft University of Technology - Delft Institute of Applied Mathematics (DIAM)

Pasquale Cirillo

ZHAW School of Management and Law

Cornelis W. Oosterlee

Utrecht University - Faculty of Science

Date Written: February 24, 2020

Abstract

An alternative generating mechanism for non-strict bivariate Archimedean copulas via the Lorenz curve of a positive random variable is proposed. Lorenz curves have been extensively studied in economics and statistics to characterize wealth inequality and tail risk. In this paper, these curves are seen as integral transforms generating increasing convex functions in the unit square.

Many of the properties of these "Lorenz copulas", from tail dependence and stochastic ordering, to their Kendall distribution function and the size of the singular part, depend on simple features of the random variable associated to the generating Lorenz curve. For instance, by selecting random variables with lower bound at zero it is possible to create copulas with asymptotic upper tail dependence.

An "alchemy" of Lorenz curves that can be used as general framework to build multiparametric families of copulas is also discussed.

Keywords: Copula, Lorenz Curve, Lorenz Copula, Kendall's tau, Generator

JEL Classification: C10, C46

Suggested Citation

Fontanari, Andrea and Cirillo, Pasquale and Oosterlee, Cornelis W., Lorenz-Generated Bivariate Archimedean Copulas (February 24, 2020). Available at SSRN: https://ssrn.com/abstract=3391514 or http://dx.doi.org/10.2139/ssrn.3391514

Andrea Fontanari

Delft University of Technology - Delft Institute of Applied Mathematics (DIAM) ( email )

Mekelweg 4
Delft, Holland 2628
Netherlands

Pasquale Cirillo (Contact Author)

ZHAW School of Management and Law ( email )

St.-Georgen-Platz 2
Winterthur, 8401
Switzerland

Cornelis W. Oosterlee

Utrecht University - Faculty of Science

Vredenburg 138
Utrecht, 3511 BG
Netherlands

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