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

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).