Max- and min-stability under first-order stochastic dominance
Abstract
Max-stability is the property that taking a maximum between two inputs results in a maximum between two outputs. We study max-stability with respect to first-order stochastic dominance, the most fundamental notion of stochastic dominance in decision theory. Under two additional standard axioms of nondegeneracy and lower semicontinuity, we establish a representation theorem for functionals satisfying max-stability, which turns out to be represented by the supremum of a bivariate function. A parallel characterization result for min-stability, that is, with the maximum replaced by the minimum in max-stability, is also established. By combining both max-stability and min-stability, we obtain a new characterization for a class of functionals, called the Lambda-quantiles, that appear in finance and political science.
Cite
@article{arxiv.2403.13138,
title = {Max- and min-stability under first-order stochastic dominance},
author = {Christopher Chambers and Alan Miller and Ruodu Wang and Qinyu Wu},
journal= {arXiv preprint arXiv:2403.13138},
year = {2025}
}