Set-valued loss-based risk measures

Abstract

In this paper, we introduce a new class of set-valued risk measures, named set-valued convex loss-based risk measures. Representation results are provided. This new class can be considered as a set-valued extension of those introduced by Cont et al. (Stat Risk Model Appl Finance Insur 30(2):133–167, 2013) and Chen et al. (Positivity, 2017). Finally, examples are also given to illustrate the set-valued convex loss-based risk measures.