  We investigate a stochastic program with expected value constraints,
addressing the problem in a general context through Distributionally Robust
Optimization (DRO) approach using Wasserstein distances, where the ambiguity
set depends on the decision variable. We demonstrate that this approach can be
reformulated into a finite-dimensional optimization problem, which, in certain
instances, can be convex. Moreover, we establish criteria for determining the
feasibility of the problem concerning the Wasserstein radius and the parameter
governing the constraint. Finally, we present numerical results within the
context of portfolio optimization. In particular, we highlight the distinctions
between our approach and several existing non-robust methods, using both
simulated data and real financial market data.
