Multivariate Shortfall and Divergence Risk Statistics

The aim of this paper is to construct two new classes of multivariate risk statistics, and to study their properties. We, first, introduce the multivariate shortfall risk statistics and multivariate divergence risk statistics. Then, their basic properties are studied, and their representation result...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2019-11, Vol.21 (11), p.1031
Main Authors: Song, Haiyan, Zeng, Xianfu, Chen, Yanhong, Hu, Yijun
Format: Article
Language:English
Subjects:
(multivariate) divergence risk statistics
(multivariate) shortfall risk statistics
convex risk statistics
entropic risk measures
entropy-like risk statistics
Euclidean space
Multivariate analysis
Random variables
representation results
Risk
risk measures
Statistics
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Summary:The aim of this paper is to construct two new classes of multivariate risk statistics, and to study their properties. We, first, introduce the multivariate shortfall risk statistics and multivariate divergence risk statistics. Then, their basic properties are studied, and their representation results are provided. Furthermore, their coherency is also characterized by means of the corresponding loss function. Finally, entropic risk statistics are given to illustrate the proposed new classes of multivariate risk statistics. The relationship between multivariate shortfall and divergence risk statistics is also discussed.
ISSN:1099-4300
1099-4300
DOI:10.3390/e21111031