We investigate two different constructions of robust Orlicz spaces as a generalisation of robust L^p-spaces. Our first construction is top-down and considers the maximal domain of a worst-case Luxemburg norm. From an applied persepective, this approach can be justified by a uniform-boundedness-type result. In typical situations, the worst-case Orlicz space agrees with the intersection of the corresponding individual Orlicz spaces. Our second construction produces the closure of a space of test random variables with respect to the worst-case Luxemburg norm. We show that separability of such spaces or their subspaces has very strong implications in terms of  dominatedness of the set of priors and thus for applications in the field of robust finance. For instance, norm closures of bounded continuous functions  as considered in the G-framework  lead to spaces which are lattice-isomorphic to sublattices of a classical L^1-space lacking, however, Dedekind \sigma-completeness . We further show that the topological spanning power of options is always limited under nondominated uncertainty.
We investigate robust Orlicz spaces as a generalisation of robust L^p-spaces. Two constructions of such spaces are distinguished, a top-down approach and a bottom-up approach. We show that separability of robust Orlicz spaces or their subspaces has very strong implications in terms of the dominatedness of the set of priors and the lack of order completeness. Our results have subtle implications for the field of robust finance. For instance, norm closures of bounded continuous functions with respect to the worst-case L^p-norm, as considered in the G-framework , lead to spaces which are lattice isomorphic to a sublattice of a classical L^1-space lacking, however, any form of order completeness . We further show that the topological spanning power of options is always limited under nondominated uncertainty.
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Our first construction is top-down and considers the maximal domain of
Two constructions of such spaces are distinguished,
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worst-case Luxemburg norm. From an applied persepective, this approach can be justified by a uniform-boundedness-type result. In typical situations, the worst-case Orlicz space agrees with the intersection of the corresponding individual Orlicz spaces. Our second construction produces the closure of a space of test random variables with respect to the worst-case Luxemburg norm.
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the lack of order completeness. Our results have subtle implications for
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with respect to the worst-case L^p-norm,
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Dedekind \sigma-completeness
any form of order completeness