Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/312211 
Year of Publication: 
2022
Citation: 
[Journal:] Mathematics and Financial Economics [ISSN:] 1862-9660 [Volume:] 16 [Issue:] 3 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2022 [Pages:] 447-480
Publisher: 
Springer, Berlin, Heidelberg
Abstract: 
We establish general "collapse to the mean" principles that provide conditions under which a law-invariant functional reduces to an expectation. In the convex setting, we retrieve and sharpen known results from the literature. However, our results also apply beyond the convex setting. We illustrate this by providing a complete account of the "collapse to the mean" for quasiconvex functionals. In the special cases of consistent risk measures and Choquet integrals, we can even dispense with quasiconvexity. In addition, we relate the "collapse to the mean" to the study of solutions of a broad class of optimisation problems with law-invariant objectives that appear in mathematical finance, insurance, and economics. We show that the corresponding quantile formulations studied in the literature are sometimes illegitimate and require further analysis.
Subjects: 
Law invariance
Quasiconvex functionals
Consistent risk measures
Nonconvex Choquet integrals
Optimisation problems
JEL: 
C61
D81
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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