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Existence of solutions for a class of bilevel stochastic linear programs

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  • Claus, Matthias

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.

Suggested Citation

  • Claus, Matthias, 2022. "Existence of solutions for a class of bilevel stochastic linear programs," European Journal of Operational Research, Elsevier, vol. 299(2), pages 542-549.
    • Handle: RePEc:eee:ejores:v:299:y:2022:i:2:p:542-549
    DOI: 10.1016/j.ejor.2021.12.004
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    References listed on IDEAS

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    1. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    2. Kovacevic, Raimund M. & Pflug, Georg Ch., 2014. "Electricity swing option pricing by stochastic bilevel optimization: A survey and new approaches," European Journal of Operational Research, Elsevier, vol. 237(2), pages 389-403.
    3. M. Kaina & L. Rüschendorf, 2009. "On convex risk measures on L p -spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 475-495, July.
    4. Alexei A. Gaivoronski & Adrian Werner, 2012. "Stochastic Programming Perspective on the Agency Problems Under Uncertainty," Lecture Notes in Economics and Mathematical Systems, in: Yuri Ermoliev & Marek Makowski & Kurt Marti (ed.), Managing Safety of Heterogeneous Systems, edition 127, pages 137-167, Springer.
    5. Patrick Cheridito & Tianhui Li, 2009. "Risk Measures On Orlicz Hearts," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 189-214, April.
    6. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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