Best-possible bounds on the set of copulas with a given value of Gini’s gamma

In this note, pointwise best-possible (lower and upper) bounds on the set of copulas with a given value of the Gini’s gamma coefficient are established. It is shown that, unlike the best-possible bounds on the set of copulas with a given value of other known measures such as Kendall’s tau, Spearman’s rho or Blomqvist’s beta, the bounds found are not necessarily copulas, but proper quasi-copulas.