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