Concave/convex weighting and utility functions for risk: A new light on classical theorems

Peter P. Wakker*, Jingni Yang

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
28 Downloads (Pure)


This paper analyzes concave and convex utility and probability distortion functions for decision under risk (law-invariant functionals). We characterize concave utility for virtually all existing models, and concave/convex probability distortion functions for rank-dependent utility and prospect theory in complete generality, through an appealing and well-known condition (convexity of preference, i.e., quasiconcavity of the functional). Unlike preceding results, we do not need to presuppose any continuity, let be differentiability. An example of a new light shed on classical results: whereas, in general, convexity/concavity with respect to probability mixing is mathematically distinct from convexity/concavity with respect to outcome mixing, in Yaari's dual theory (i.e., Wang's premium principle) these conditions are not only dual, as was well-known, but also logically equivalent, which had not been known before.

Original languageEnglish
Pages (from-to)429-435
Number of pages7
JournalInsurance: Mathematics and Economics
Publication statusPublished - 1 Sept 2021

Bibliographical note

JEL classification: D81, C60

Publisher Copyright:
© 2021 The Author(s)


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