Strongly consistent multivariate conditional risk measures

Hoffmann, Hannes; Meyer-Brandis, Thilo und Svindland, Gregor (2018): Strongly consistent multivariate conditional risk measures. In: Mathematics and Financial Economics, Bd. 12, Nr. 3: S. 413-444

Abstract

We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure as introduced Hoffmann et al. (Stoch Process Appl 126(7): 2014-2037, 2016). Further, in analogy to the univariate case in Follmer (Stat Risk Model 31(1): 79-103, 2014), we prove that under law-invariance strong consistency implies that multivariate conditional risk measures are necessarily multivariate conditional certainty equivalents.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Finanz- und Versicherungsmathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1862-9679
• Sprache: Englisch