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Preferences over all random variables: Incompatibility of convexity and continuity

Hirbod Assa and Alexander Zimper

Journal of Mathematical Economics, 2018, vol. 75, issue C, 71-83

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.

Keywords: Large spaces; Preference for diversification; Utility representations (search for similar items in EconPapers)
Date: 2018
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Working Paper: Preferences Over all Random Variables: Incompatibility of Convexity and Continuity (2017) Downloads
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Handle: RePEc:eee:mateco:v:75:y:2018:i:c:p:71-83