Separability Versus Robustness of Orlicz Spaces: Financial and Economic Perspectives

Liebrich, Felix-Benedikt und Nendel, Max (2022): Separability Versus Robustness of Orlicz Spaces: Financial and Economic Perspectives. In: SIAM Journal on Financial Mathematics, Bd. 13, Nr. 4: S. 1344-1378

Abstract

We investigate robust Orlicz spaces as a generalization of robust Lp-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 Lp-norm, as considered in the G-framework, lead to spaces which are lattice isomorphic to a sublattice of a classical L1-space lacking, however, any form of order completeness. We further show that the topological spanning power of options is always limited under nondominated uncertainty.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Finanz- und Versicherungsmathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1945-497X
• Sprache: Englisch