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Preferences Over all Random Variables: Incompatibility of Convexity and Continuity

Hirbod Assa () and Alexander Zimper
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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

No 201714, Working Papers from University of Pretoria, Department of Economics

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.

Keywords: Large Space; Preference for Diversification; Utility Representation; Risk Measures (search for similar items in EconPapers)
JEL-codes: D81 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-mic and nep-upt
Date: 2017-03
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