Bounds for the Clayton copula
Articles
Martynas Manstavičius
Vilnius University
Remigijus Leipus
Vilnius University
https://orcid.org/0000-0002-2099-2380
Published 2017-03-15
https://doi.org/10.15388/NA.2017.2.7
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Keywords

Archimedean copula
Clayton copula
copula bounds
negative dependence

How to Cite

Manstavičius M. and Leipus R. (2017) “Bounds for the Clayton copula”, Nonlinear Analysis: Modelling and Control, 22(2), pp. 248-260. doi: 10.15388/NA.2017.2.7.

Abstract

We provide two upper bounds on the Clayton copula Cθ(u1,...,un) if θ > 0 and n ≥ 2 and a lower bound in the case θ ∈ [-1,0) and n ≥ 2. The obtained bounds provide a nice probabilistic interpretation related to some negative dependence structures and also allow defining three new two-dimensional copulas which tighten the classical Fréchet–Hoeffding bounds for the Clayton copula when n = 2.

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