On all Pickands Dependence Functions whose corresponding Extreme-Value-Copulas have Spearman ρ (Kendall τ) identical to some value v ∈ [0,1]

01/23/2018

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by   Noppadon Kamnitui, et al.

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We answer an open question posed by the second author at the Salzburg workshop on Dependence Models and Copulas in 2016 concerning the size of the family A^ρ_v (A^τ_v) of all Pickands dependence functions A whose corresponding Extreme-Value-Copulas have Spearman ρ (Kendall τ) equal to some arbitrary, fixed value v ∈ [0,1]. After determining compact sets Ω^ρ_v, Ω^τ_v ⊆ [0,1] × [1/2,1] containing the graphs of all Pickands dependence functions from the classes A^ρ_v and A^τ_v respectively, we then show that both sets are best possible.