Fatou property of risk measures on Orlicz spaces

For a coherent risk measure ρ on the space of bounded random variables, Delbaen (2002) proved that ρ can be represented as the worst expectation over a class of probabilities whenever ρ has the Fatou property. Lately,... [ view full abstract ]

For a coherent risk measure ρ on the space of bounded random variables, Delbaen (2002) proved that ρ can be represented as the worst expectation over a class of probabilities whenever ρ has the Fatou property. Lately, it has been asked whether Delbaen's representation theorem holds on more general model spaces, specifically, Orlicz spaces. In this talk, we present a comprehensive investigation on this problem. We show that theorem fails in general and remains valid if if the risk measure possess additional properties (e.g., law-invariance, strong Fatou property).