Moment inequalities for higher-order (inverse) stochastic dominance

TL;DR

This paper develops necessary moment inequality conditions for higher-order inverse stochastic dominance and explores how background risk variables affect higher-order stochastic dominance, extending previous results to higher orders.

Contribution

It introduces necessary conditions involving moment inequalities for higher-order inverse stochastic dominance and generalizes the influence of background risk to higher orders.

Findings

Necessary moment inequalities for inverse stochastic dominance

Extension of background risk effects to higher-order stochastic dominance

Generalization of previous results to higher orders

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.