Nonlinear Analysis: Modelling and Control
Vol. 22, No. 2
Martynas Manstavičius, Remigijus Leipus
Bounds for the Clayton copula
doi:10.15388/NA.2017.2.7
Received  2016-02-09  /   Revised  2016-10-04  /   Accepted   2016-10-05
Published Online  2017-01-19
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.
Keywords:
Archimedean copula, Clayton copula, copula bounds, negative dependence.