  This work presents a new Distributionally Robust Optimization approach, using
$p$-Wasserstein metrics, to analyze a stochastic program in a general context.
The ambiguity set in this approach depends on the decision variable and is
represented as a ball where both the center and the radius depend on the
decision variable. We show that, under Lipschitz's assumptions for the
objective function, our approach can be reformulated as a finite-dimensional
optimization problem, which is sometimes convex. In addition, we numerically
compare our proposed approach with the standard formulation of distributionally
robust optimization, which typically does not use ambiguity sets dependent on
the decision variable, in the context of portfolio optimization.
