  We consider bilevel linear problems, where the right-hand side of the lower
level problems is stochastic. The leader has to decide in a here-and-now
fashion, while the follower has complete information. In this setting, the
leader's outcome can be modeled by a random variable, which gives rise to a
broad spectrum of models involving coherent or convex risk measures and
stochastic dominance constraints. We outline Lipschitzian properties,
conditions for existence and optimality, as well as stability results.
Moreover, for finite discrete distributions, we discuss the special structure
of equivalent deterministic bilevel programs and its potential use to mitigate
the curse of dimensionality.
