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Max-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 investigate 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 monotonicity 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. Our characterized functionals encompass special classes of functionals in the literature of risk measures, such as benchmark-loss Value at Risk (VaR) and $\Lambda$-quantile.

Suggested Citation

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

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