Two stochastic dominance criteria based on tail comparisons

Abstract

Actuarial risks and financial asset returns are typically heavy tailed. In this paper, we introduce 2 stochastic dominance criteria, called the right‐tail order and the left‐tail order, to compare these variables stochastically. The criteria are based on comparisons of expected utilities, for 2 classes of utility functions that give more weight to the right or the left tail (depending on the context) of the distributions. We study their properties, applications, and connections with other classical criteria, including the increasing convex and the second‐order stochastic dominance. Finally, we rank some parametric families of distributions and provide empirical evidence of the new stochastic dominance criteria with an example using real data.