Before revision:  Specifically, an investor considers alternative strategies that co-move with the benchmark and whose terminal wealth lies within a Wasserstein ball surrounding  it.
After revision:  Specifically, an investor considers alternative strategies that co-move with the benchmark and whose terminal wealth lies within a Wasserstein ball surrounding a benchmark's -- being distributionally close -- and that have a specified dependence/copula -- tying state-by-state outcomes -- to it.