Consistency of Distributionally Robust Risk- and Chance-Constrained Optimization Under Wasserstein Ambiguity Sets

We study stochastic optimization problems with chance and risk constraints, where in the latter, is quantified terms of conditional value-at-risk (CVaR). consider distributionally robust versions these problems, constraints are required to hold for a family distributions constructed from observed realizations uncertainty via Wasserstein distance. Our main results establish that if samples drawn independently an underlying distribution satisfy suitable technical assumptions, then optimal value optimizers converge respective quantities original as sample size increases.