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Preferences over all random variables: Incompatibility of convexity and continuity

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  • Assa, Hirbod
  • Zimper, Alexander

Abstract

We consider preferences over all random variables on a given nonatomic probability space. We show that non-trivial and complete preferences cannot simultaneously satisfy the two fundamental principles of convexity and continuity. As an implication of this incompatibility result there cannot exist any non-trivial continuous utility representations over all random variables that are either quasi-concave or quasi-convex. This rules out standard risk-averse (or seeking) utility representations for this large space of random variables.

Suggested Citation

  • Assa, Hirbod & Zimper, Alexander, 2018. "Preferences over all random variables: Incompatibility of convexity and continuity," Open Access Publications from Kiel Institute for the World Economy 233948, Kiel Institute for the World Economy (IfW Kiel).
    • Handle: RePEc:zbw:ifwkie:233948
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    Cited by:

    1. Carole Bernard & Gero Junike & Thibaut Lux & Steven Vanduffel, 2024. "Cost-efficient payoffs under model ambiguity," Finance and Stochastics, Springer, vol. 28(4), pages 965-997, October.
    2. Metin Uyanik & Aniruddha Ghosh & M. Ali Khan, 2023. "Separately Convex and Separately Continuous Preferences: On Results of Schmeidler, Shafer, and Bergstrom-Parks-Rader," Papers 2310.00531, arXiv.org.
    3. Alexander Zimper & Hirbod Assa, 2019. "Preferences Over Rich Sets of Random Variables: Semicontinuity in Measure versus Convexity," Working Papers 201940, University of Pretoria, Department of Economics.

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    More about this item

    Keywords

    large spaces; preference for diversification; utility representations;
    All these keywords.

    JEL classification:

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

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