# 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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**Related works:**

Working Paper: Preferences Over all Random Variables: Incompatibility of Convexity and Continuity (2017)

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:mateco:v:75:y:2018:i:c:p:71-83

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