Systemic risk statistics with scenario analysis.

In this paper, we introduce two new classes of risk statistics, named convex and positively homogeneous systemic risk statistics, respectively. Structural decomposition results and representation results for them are provided. These new risk statistics can be considered as a kind of systemic risk extension of risk statistics introduced by Kou, Peng, and Heyde, and also empirical versions of system risk measures introduced by Cehn, Iyengar, and Mollemi and Kromer, Overbeck, and Zich. Finally, some examples are also given. [ABSTRACT FROM AUTHOR]