Journal Article

Preferences Over All Random Variables: Incompatibility of Convexity and Continuity


  • Assa
  • H.
  • Zimper
  • A.
Publication Date

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.


Key Words

  • Large spaces
  • Preference for diversification
  • Utility representations