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...

We extend the characterization of the left-monotone risk aversion developed by Ryan (2006) to the case of unbounded random variables. The notion of weak convergence is insufficient for such an extension. It requires the solution of a host of delicate convergence problems. To this end, some...