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Hoffmann, Hannes; Meyer-Brandis, Thilo; Svindland, Gregor (2018): Strongly consistent multivariate conditional risk measures. In: Mathematics and Financial Economics, Vol. 12, No. 3: pp. 413-444
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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.