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Two Moments for Risk-Monotone Additive Statistics

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  • Mark Whitmeyer

Abstract

Every statistic on laws with finite pth moment that is additive across independent risks and monotone in mean-preserving spreads depends only on an additive function of the mean when p is strictly less than 2, and only on such a function and a nonnegative multiple of the variance when p is no less than 2.

Suggested Citation

  • Mark Whitmeyer, 2026. "Two Moments for Risk-Monotone Additive Statistics," Papers 2608.10883, arXiv.org.
    • Handle: RePEc:arx:papers:2608.10883
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    File URL: https://arxiv.org/pdf/2608.10883
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    References listed on IDEAS

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    1. Xiaosheng Mu & Luciano Pomatto & Philipp Strack & Omer Tamuz, 2024. "Monotone Additive Statistics," Econometrica, Econometric Society, vol. 92(4), pages 995-1031, July.
    2. Xiaosheng Mu & Luciano Pomatto & Philipp Strack & Omer Tamuz, 2021. "Monotone additive statistics," Papers 2102.00618, arXiv.org, revised Apr 2024.
    3. Luciano Pomatto & Philipp Strack & Omer Tamuz, 2020. "Stochastic Dominance under Independent Noise," Journal of Political Economy, University of Chicago Press, vol. 128(5), pages 1877-1900.
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