Archimedean copulae and positive dependence

By Alfred Müller, Marco Scarsini. 2005

156 citations recorded by the source corpus.

In this paper, we consider different issues related to Archimedean copulae and positive dependence. In the first part, we characterize Archimedean copulae that possess positive dependence properties such as multivariate total positivity of order 2 (MTP2) and conditionally increasingness in sequence. In the second part, we investigate conditions for exchangeable binary sequences to admit an Archimedean copula, and we show that they depend on the extendibility of the sequence, and therefore on its positive-dependence properties.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/1a08e18c2b4eac61e3144a0d06cf15797768a145

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Citations in the corpus

Total positivity in Markov structures (2015, background): “There is some related work in the context of copulae [27].”
Inference in multivariate Archimedean copula models (2011, background): “However, it is still unclear how the distributional properties of R relate to earlier results on classical stochastic orderings of Archimedean copulas; see, e.g., Genest and MacKay (1986), Caperaa and Genest (1993), Wei and Hu (2002) or Muller and Scarsini (2005) and references therein.”
Stochastic comparisons on sample extremes of dependent and heterogenous observations (2016, methodology): “For more details on log-convexity and log-concavity of generators of Archimedean copulas, one may refer to Bassan and Spizzichino [27] and Müller and Scarsini.[28] These three lemmas will be employed to develop the proofs of main results in Sections 4 and 5.”
A Comparative Analysis of CDO Pricing Models under the Factor Copula Framework (2009, methodology): “Then, as a consequence of the Ky Fan–Lorentz theorem, we have: where ≤dcx holds for the directional convex order (see Müller and Stoyan [2002] or Rüschendorf [2004] for details).”
Multivariate Archimedean copulas, $d$-monotone functions and $\ell_1$-norm symmetric distributions (2009, background): “Some authors [14, 26, 28] have required that ψ only has derivatives up to order d which alternate in sign, a condition which, though sufficient and considerably weaker, is still not necessary.”
Some positive dependence stochastic orders (2006, unknown): “Proposition 2.20 is of interest in comparison to results of Müller and Scarsini (2003).”
Lower tail dependence for Archimedean copulas: Characterizations and pitfalls (2007, unknown): “A versatile subclass of copulas is the one of Archimedean copulas, introduced in Kimberling (1974) and studied intensively since (e.g. Genest and MacKay, 1986; Genest and Rivest, 1993; M¨uller and Scarsini, 2004).”