2024/03/19 by Chambers, Christopher, Miller, Alan, Wang, Ruodu +1 · 1 citation
#FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Probability (math.PR)
paper · doi:10.48550/arxiv.2403.13138
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.