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Preferences Over all Random Variables: Incompatibility of Convexity and Continuity

Author

Listed:
  • Hirbod Assa

    () (Institute for Financial and Actuarial Mathematics and Institute for Risk and Uncertainty, University of Liverpool, Center for Doctoral Training, Chadwick Building, Liverpool, UK)

  • Alexander Zimper

    () (Department of Economics, University of Pretoria, South Africa, and Kiel Institute for the World Economy, Germany)

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 risk-averse (or seeking) expected utility representations and, more generally, risk- and uncertainty-averse (or seeking) Choquet expected utility representations for this large space of random variables.

Suggested Citation

  • Hirbod Assa & Alexander Zimper, 2017. "Preferences Over all Random Variables: Incompatibility of Convexity and Continuity," Working Papers 201714, University of Pretoria, Department of Economics.
  • Handle: RePEc:pre:wpaper:201714
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    More about this item

    Keywords

    Large Space; Preference for Diversification; Utility Representation; Risk Measures;

    JEL classification:

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

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