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Open AccessArticle

Multivariate Shortfall and Divergence Risk Statistics

1
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
2
College of Finance and Statistics, Hunan University, Changsha 410082, China
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Author to whom correspondence should be addressed.
Entropy 2019, 21(11), 1031; https://doi.org/10.3390/e21111031
Received: 22 September 2019 / Revised: 16 October 2019 / Accepted: 22 October 2019 / Published: 24 October 2019
(This article belongs to the Section Information Theory, Probability and 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 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. View Full-Text
Keywords: risk measures; entropic risk measures; convex risk statistics; (multivariate) shortfall risk statistics; (multivariate) divergence risk statistics; entropy-like risk statistics; representation results risk measures; entropic risk measures; convex risk statistics; (multivariate) shortfall risk statistics; (multivariate) divergence risk statistics; entropy-like risk statistics; representation results
MDPI and ACS Style

Song, H.; Zeng, X.; Chen, Y.; Hu, Y. Multivariate Shortfall and Divergence Risk Statistics. Entropy 2019, 21, 1031.

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