Dual Representation of Robust Risk Measures and Uncertainty Sets

Marlon R. Moresco, Marcelo Righi and Silvana M. Pesenti

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Abstract: We consider robust risk measures that arise as worst-case values of convex risk measures evaluated on uncertainty sets. We characterize continuity properties of robust risk measures through their consolidated uncertainty sets, derive dual representations for robust risk measures, and develop a set-valued dual representation for consolidated uncertainty sets. The two dual frameworks rely on distinct geometric assumptions and are therefore complementary rather than interchangeable.

Date: 2026-06
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