Strongly consistent multivariate conditional risk measures

  • Hannes Hoffmann
  • Thilo Meyer-Brandis
  • Gregor Svindland
Article
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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 Föllmer (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.

Keywords

Multivariate risk measures Strong consistency Law-invariance Conditional certainty equivalents Systemic risk measures 

Mathematics Subject Classification

G10 G32 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MunichMunichGermany

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