Loss-based risk statistics with scenario analysis

Since the investors and regulators pay more attention to losses rather than gains, we will study a new class of risk statistics, named loss-based risk statistics in this paper. This new class of risk statistics can be considered as a kind of risk extension of risk statistics introduced by Kou, Peng and Heyde (2013), and also data-based versions of loss-based risk measures introduced by Cont et al. (2013) and Sun et al. (2018).