Preferences over all random variables: Incompatibility of convexity and continuity



Assa, Hirbod and Zimper, Alexander
(2018) Preferences over all random variables: Incompatibility of convexity and continuity. JOURNAL OF MATHEMATICAL ECONOMICS, 75 (C). pp. 71-83.

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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.

Item Type: Article
Uncontrolled Keywords: Large spaces, Preference for diversification, Utility representations
Depositing User: Symplectic Admin
Date Deposited: 15 Aug 2018 09:57
Last Modified: 19 Jan 2023 01:28
DOI: 10.1016/j.jmateco.2017.12.006
Open Access URL: https://repository.up.ac.za/handle/2263/64454?show...
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3025023