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

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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 Aρᵥ (Aτᵥ) 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 Ωρᵥ, Ωτᵥ [0,1] × [1/2,1] containing the graphs of all Pickands dependence functions from the classes Aρᵥ and Aτᵥ respectively, we then show that both sets are best possible.