Moment inequalities for higher-order (inverse) stochastic dominance

Abstract: Stochastic dominance has been studied extensively, particularly in the finance and economics literature. In this paper, we obtain two results. First, necessary conditions for higher-order inverse stochastic dominance are developed. These conditions, which involve moment inequalities of the minimum order statistics, are analogous to the ones obtained by Fishburn (1980b) for usual higher-order stochastic dominance. Second, we investigate how background risk variables influence usual higher-order stochastic dominance. The main result generalizes the ones in Pomatto et al. (2020) from the first-order and second-order stochastic dominance to the higher-order.