Multivariate convex risk statistics with scenario analysis

Wei Liu, Linxiao Wei and Yijun Hu

Communications in Statistics - Theory and Methods, 2019, vol. 48, issue 22, 5585-5601

Abstract: In this article, we introduce three new classes of multivariate risk statistics, which can be considered as data-based versions of multivariate risk measures. These new classes are multivariate convex risk statistics, multivariate comonotonic convex risk statistics and multivariate empirical-law-invariant convex risk statistics, respectively. Representation results are provided. The arguments of proofs are mainly developed by ourselves. It turns out that all the relevant existing results in the literature are special cases of those obtained in this article.

Date: 2019
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DOI: 10.1080/03610926.2018.1515957

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