Preferences over all random variables: Incompatibility of convexity and continuity - Hirbod Assa; Alexander Zimper (Journal of Mathematical Economics, 2018)
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: D81; 330; large spaces; preference for diversification; utility representations