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Stochastic Dominance Analysis without the Independence Axiom

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  • Simone Cerreia Vioglio
  • Fabio Maccheroni
  • Massimo Marinacci

Abstract

We characterize the consistency of a large class of nonexpected utility preferences (including mean-variance preferences and prospect theory preferences) with stochastic orders (for example, stochastic dominances of different degrees). Our characterization rests on a novel decision theoretic result that provides a behavioral interpretation of the set of all derivatives of the functional representing the decision maker's preferences. As an illustration, we consider in some detail prospect theory and choice-acclimating preferences, two popular models of reference dependence under risk, and we show the incompatibility of loss aversion with prudence. JEL classification: D81 Keywords: Stochastic dominance, integral stochastic orders, nonexpected utility, risk aversion, multi-utility representation, prospect theory, choice-acclimating personal equilibria

Suggested Citation

  • Simone Cerreia Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "Stochastic Dominance Analysis without the Independence Axiom," Working Papers 549, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    • Handle: RePEc:igi:igierp:549
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    Cited by:

    1. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2020. "Utilitarianism with and without expected utility," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 77-113.
    2. Cerreia-Vioglio, Simone & Dillenberger, David & Ortoleva, Pietro, 2020. "An explicit representation for disappointment aversion and other betweenness preferences," Theoretical Economics, Econometric Society, vol. 15(4), November.
    3. Daniel Krähmer, 2024. "The Hold-Up Problem with Flexible Unobservable Investments," ECONtribute Discussion Papers Series 278, University of Bonn and University of Cologne, Germany.
    4. Felix-Benedikt Liebrich & Cosimo Munari, 2022. "Law-Invariant Functionals that Collapse to the Mean: Beyond Convexity," Mathematics and Financial Economics, Springer, volume 16, number 2, June.
    5. Simone Cerreia-Vioglio & Efe A. Ok, 2018. "The Rational Core of Preference Relations," Working Papers 632, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    6. Benjamin Balzer & Antonio Rosato, 2021. "Expectations-Based Loss Aversion in Auctions with Interdependent Values: Extensive vs. Intensive Risk," Management Science, INFORMS, vol. 67(2), pages 1056-1074, February.

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    More about this item

    Keywords

    stochastic dominance; integral stochastic orders; nonexpected utility; risk aversion; multi-utility representation; prospect theory; choice-acclimating personal equilibria;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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