Existence of solutions for a class of bilevel stochastic linear programs

Abstract

We study bilevel stochastic linear programs where the upper and lower level goal functions as well as the right-hand side of the follower’s constraint system are affected by randomness. Invoking a robust representation result, we prove that any objective functional derived from a convex risk measure is lower semicontinuous, even if the underlying distribution is not absolutely continuous with respect to the Lebesgue measure. Moreover, we provide a continuity result that also applies to pessimistic models and show that the existence of solutions can be guaranteed under standard compactness assumptions.