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Stochastic Dominance Under Independent Noise

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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, etc.) 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.

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  • Luciano Pomatto & Philipp Strack & Omer Tamuz, 2018. "Stochastic Dominance Under Independent Noise," Papers 1807.06927, arXiv.org, revised May 2019.
    • Handle: RePEc:arx:papers:1807.06927
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    1. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    2. Alexey Kushnir, 2013. "On the equivalence between Bayesian and dominant strategy implementation: the case of correlated types," ECON - Working Papers 129, Department of Economics - University of Zurich.
    3. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    4. Alex Gershkov & Jacob K. Goeree & Alexey Kushnir & Benny Moldovanu & Xianwen Shi, 2013. "On the Equivalence of Bayesian and Dominant Strategy Implementation," Econometrica, Econometric Society, vol. 81(1), pages 197-220, January.
    5. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-1123, September.
    6. Diamond, Peter A, 1998. "Optimal Income Taxation: An Example with a U-Shaped Pattern of Optimal Marginal Tax Rates," American Economic Review, American Economic Association, vol. 88(1), pages 83-95, March.
    7. Quiggin, John, 1991. "Comparative Statics for Rank-Dependent Expected Utility Theory," Journal of Risk and Uncertainty, Springer, vol. 4(4), pages 339-350, December.
    8. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
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    Cited by:

    1. Fabio Maccheroni & Massimo Marinacci & Ruodu Wang & Qinyu Wu, 2023. "Risk Aversion and Insurance Propensity," Papers 2310.09173, arXiv.org, revised Jul 2024.
    2. Marilyn Pease & Mark Whitmeyer, 2024. "How to Make an Action Better," Papers 2408.09294, arXiv.org, revised Nov 2024.
    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. Chambers, Christopher P. & Echenique, Federico, 2020. "Spherical preferences," Journal of Economic Theory, Elsevier, vol. 189(C).
    5. Xiaosheng Mu & Luciano Pomatto & Philipp Strack & Omer Tamuz, 2024. "Monotone Additive Statistics," Econometrica, Econometric Society, vol. 92(4), pages 995-1031, July.
    6. 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.
    7. Xiaosheng Mu & Luciano Pomatto & Philipp Strack & Omer Tamuz, 2021. "Monotone additive statistics," Papers 2102.00618, arXiv.org, revised Apr 2024.

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