Set-valued risk statistics with scenario analysis

• DOI: 10.1016/j.spl.2017.08.004
• Publication Date: 2017-08-15T11:31:09Z
• Authors: Yanhong Chen; Yijun Hu
• Keywords: 0211 other engineering and technologies; 02 engineering and technology

Abstract In this paper, we introduce two new classes of risk statistics, named set-valued coherent and convex risk statistics. These new risk statistics can be considered as a kind of set-valued extension of risk statistics introduced by Kou, Peng and Heyde (2013), and also empirical versions of set-valued coherent and convex risk measures introduced by Jouini, Meddeb and Touzi (2004) and Hamel (2009), respectively. Representation results for these new introduced risk statistics are provided. Finally, we also provide some examples of set-valued coherent and convex risk statistics.