We study monotone convex functions ψ : L0 (Ω, F, P) → (−∞, ∞], and derive a dual representation as well as conditions that ensure the existence of a σ-additive subgradient. The results are motivated by applications in economic agents’choice theory.
We give robust representations of law-invariant monotone quasiconvex functions.
The results are based on works by Jouini et al. and Svindland, showing that lawinvariant
quasiconvex functions have the Fatou property.