Preferences over rich sets of random variables: on the incompatibility of convexity and semicontinuity in measure



Zimper, Alexander and Assa, Hirbod
(2020) Preferences over rich sets of random variables: on the incompatibility of convexity and semicontinuity in measure. Mathematics and Financial Economics, 2020.

[img] Text
continuity-16August2020.pdf - Accepted Version

Download (272kB) | Preview

Abstract

This paper considers a decision maker whose preferences are locally upper- or/and lower-semicontinuous in measure. We introduce the notion of a rich set which encompasses any standard vector space of random variables but also much smaller sets containing only random variables with at most two different outcomes in their support. Whenever preferences are complete on a rich set of random variables, lower- (resp. upper-) semicontinuity in measure becomes incompatible with convexity of strictly better (resp. worse) sets. We discuss implications for utility representations and risk-measures. In particular, we show that the value-at-risk criterion violates convexity exactly because it is lower-semicontinuous in measure.

Item Type: Article
Uncontrolled Keywords: Continuous preferences, Utility representations, Convex risk measures, Value-at-risk
Depositing User: Symplectic Admin
Date Deposited: 14 Sep 2020 08:36
Last Modified: 20 Aug 2022 11:37
DOI: 10.1007/s11579-020-00280-z
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3100854