On the C†property and w∗†representations of risk measures

Niushan Gao and Foivos Xanthos

Mathematical Finance, 2018, vol. 28, issue 2, 748-754

Abstract: We identify a large class of Orlicz spaces LΦ(μ) for which the topology σ(LΦ(μ),LΦ(μ)n∼) fails the C†property introduced by Biagini and Frittelli. We also establish a variant of the C†property and use it to prove a w∗†representation theorem for proper convex increasing functionals, satisfying a suitable version of Delbaen's Fatou property, on Orlicz spaces LΦ(μ) with limt→∞Φ(t)t=∞. Our results apply, in particular, to risk measures on all Orlicz spaces LΦ(P) other than L1(P).

Date: 2018
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