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

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  • Christopher Chambers
  • Alan Miller
  • Ruodu Wang
  • Qinyu Wu

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.

Suggested Citation

  • Christopher Chambers & Alan Miller & Ruodu Wang & Qinyu Wu, 2024. "Max- and min-stability under first-order stochastic dominance," Papers 2403.13138, arXiv.org, revised Feb 2025.
    • Handle: RePEc:arx:papers:2403.13138
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    References listed on IDEAS

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