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...

In this paper, we propose new risk measures from a regulator's perspective on the regulatory capital requirements for insurers. The proposed risk measures possess many desired properties including monotonicity, translation-invariance, positive homogeneity, subadditivity, nonnegative loading, and...

We study risk sharing games with quantile-based risk measures and heterogeneous beliefs, motivated by the use of internal models in finance and insurance. Explicit forms of Pareto-optimal allocations and competitive equilibria are obtained by solving various optimization problems. For Expected...