Existence of solutions for a class of bilevel stochastic linear programs

Matthias Claus

European Journal of Operational Research, 2022, vol. 299, issue 2, 542-549

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.

Keywords: Stochastics and statistics; Bilevel stochastic programming; Existence results; Risk aversion (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:299:y:2022:i:2:p:542-549

DOI: 10.1016/j.ejor.2021.12.004

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