A Duality Theory for Set-Valued Functions I: Fenchel Conjugation Theory

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Set-valued risk measures for conical market models (2010, methodology): “the form {X ∈ Lp d : u ∈ R(X)}, u ∈ M, are convex. Proposition 6.4 produces this fact. Fact 3. If R is closed convex and R(X0) 6= M for X0 ∈ Lp d with R(X0) 6= ∅, then R(X) 6= ∅ for all X ∈ Lp d. See [9], proposition 5. For the proof of theorem 4.2, we shall make use of the Fenchel conjugation conce”
Solution concepts in vector optimization: a fresh look at an old story (2011, background): “A further reference that deals with upper closed sets in this more general framework is the paper 14 by Hamel.”