TY - UNPB

T1 - Separability vs. robustness of Orlicz spaces

T2 - financial and economic perspectives

AU - Liebrich, Felix-Benedikt

AU - Nendel, Max

PY - 2020/9/18

Y1 - 2020/9/18

N2 - 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.

AB - 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.

KW - math.PR

KW - q-fin.MF

M3 - Preprint

BT - Separability vs. robustness of Orlicz spaces

ER -