强相合多元条件风险测度
Strongly Consistent Multivariate Conditional Risk Measures
摘要：
我们考虑强一致的多元条件风险测度族。我们证明了在强一致性下，这些族允许分解为条件聚集函数和单变量条件风险度量，如Hoffmann et al.（2016）所介绍的。此外，与Föllmer（2014）中的单变量情况类似，我们证明了在律不变性下强一致性意味着多元条件风险度量必然是多元条件确定性等价物。
英文摘要：
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. (2016). Further, in analogy to the univariate case in Föllmer (2014), we prove that under law-invariance strong consistency implies that multivariate conditional risk measures are necessarily multivariate conditional certainty equivalents.
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