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Stochastic Dominance under Independent Noise

Author

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  • Luciano Pomatto
  • Philipp Strack
  • Omer Tamuz

Abstract

Stochastic dominance is a crucial tool for the analysis of choice under risk. It is typically analyzed as a property of two gambles that are taken in isolation. We study how additional independent sources of risk (e.g., uninsurable labor risk, house price risk) can affect the ordering of gambles. We show that, perhaps surprisingly, background risk can be strong enough to render lotteries that are ranked by their expectation ranked in terms of first-order stochastic dominance. We extend our results to second-order stochastic dominance and show how they lead to a novel and elementary axiomatization of mean-variance preferences.

Suggested Citation

  • 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.
    • Handle: RePEc:ucp:jpolec:doi:10.1086/705555
    DOI: 10.1086/705555
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    Cited by:

    1. Chen, An & Müller, Alfred & Rach, Manuel, 2025. "The tontine puzzle," Journal of Mathematical Economics, Elsevier, vol. 121(C).
    2. Marilyn Pease & Mark Whitmeyer, 2024. "How to Make an Action Better," Papers 2408.09294, arXiv.org, revised Mar 2025.
    3. Anderson, Robert M. & Duanmu, Haosui & Ghosh, Aniruddha & Khan, M. Ali, 2024. "On existence of Berk-Nash equilibria in misspecified Markov decision processes with infinite spaces," Journal of Economic Theory, Elsevier, vol. 217(C).
    4. Xiaosheng Mu & Luciano Pomatto & Philipp Strack & Omer Tamuz, 2021. "From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again," Econometrica, Econometric Society, vol. 89(1), pages 475-506, January.
    5. Chambers, Christopher P. & Echenique, Federico, 2020. "Spherical preferences," Journal of Economic Theory, Elsevier, vol. 189(C).
    6. De Vecchi, Corrado & Scherer, Matthias, 2025. "Pricing insurance contracts with an existing portfolio as background risk," Insurance: Mathematics and Economics, Elsevier, vol. 122(C), pages 180-193.
    7. Fabio Maccheroni & Massimo Marinacci & Ruodu Wang & Qinyu Wu, 2023. "Risk Aversion and Insurance Propensity," Papers 2310.09173, arXiv.org, revised Feb 2025.
    8. Xiaosheng Mu & Luciano Pomatto & Philipp Strack & Omer Tamuz, 2024. "Monotone Additive Statistics," Econometrica, Econometric Society, vol. 92(4), pages 995-1031, July.
    9. Xiaosheng Mu & Luciano Pomatto & Philipp Strack & Omer Tamuz, 2021. "Monotone additive statistics," Papers 2102.00618, arXiv.org, revised Apr 2024.
    10. Xiangxin He & Fangda Liu & Ruodu Wang, 2026. "Diversification Preferences and Risk Attitudes," Papers 2601.04067, arXiv.org, revised Mar 2026.

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