On continuity in risk-averse bilevel stochastic linear programming with random lower level objective function

We study bilevel stochastic linear programs with fixed lower level feasible set and random follower's goal function and show that the parametrized random variable arising as the upper level outcome depends continuously on the leader's decision w.r.t. any L p -norm with p ∈ [ 1 , ∞ ) . This entails continuity of the objective function for a class of models involving convex risk measures defined on appropriate L p -spaces and allows to formulate verifiable sufficient conditions for the existence of optimal solutions.