On the C-property and $w^{\ast }$-representations of risk measures

Abstract

We identify a large class of Orlicz spaces $X$ for which the topology $\sigma (X,X_n^{\sim })$ fails the C-property introduced in [7]. We also establish a variant of the C-property and use it to prove a $w^{\ast }$-representation theorem for proper convex increasing functionals on dual Banach lattices that satisfy a suitable version of Delbaen's Fatou property. Our results apply, in particular, to risk measures on all Orlicz spaces over $[0,1]$ which is not $L_1[0,1]$.

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References in corpus (2)

• Uo-convergence and its applications to Cesàro means in Banach lattices
• On the Lebesgue Property of Monotone Convex Functions

Cited by in corpus (5)

• Convex duality and Orlicz spaces in expected utility maximization
• Duality for unbounded order convergence and applications
• Convex functions on dual Orlicz spaces
• Fatou Property, representations, and extensions of law-invariant risk measures on general Orlicz spaces
• Smallest order closed sublattices and option spanning