In this paper, we introduce a class of optimized certainty equivalent based on the variational preference, give its dual representation based on ϕ-divergence, and study its equivalent characterization of positive homogeneity and coherence. As applications, we investigate the properties of...

How to detect different tail behaviors of two risk random variables with the same mean is an important task. In this paper, motivated by Burzoni et al. (2022), a class of convex risk measures, called as adjusted higher-order Expected Shortfall (ES), is introduced and studied. The adjusted risk...