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Max- and min-stability under first-order stochastic dominance

Author

Listed:
  • Christopher Chambers

    (Georgetown University)

  • Alan Miller

    (Western University)

  • Ruodu Wang

    (University of Waterloo)

  • Qinyu Wu

    (University of Waterloo)

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 $$\Lambda $$ Λ -quantiles, that appear in finance and political science.

Suggested Citation

  • Christopher Chambers & Alan Miller & Ruodu Wang & Qinyu Wu, 2025. "Max- and min-stability under first-order stochastic dominance," Mathematics and Financial Economics, Springer, volume 19, number 7, December.
    • Handle: RePEc:spr:mathfi:v:19:y:2025:i:3:d:10.1007_s11579-025-00398-y
    DOI: 10.1007/s11579-025-00398-y
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