Bounds for the Clayton copula - Manstavičius, Martynas; Leipus, Remigijus (Nonlinear Analysis: Modelling and Control, 2017)
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.