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Law-Invariant Functionals that Collapse to the Mean: Beyond Convexity

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Authors

  • Felix-Benedikt Liebrich
  • Cosimo Munari

External Research Organisations

  • Universität Zürich (UZH)
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    • Citation Indexes: 7
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    • Readers: 2
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Details

Original languageEnglish
Pages (from-to)447-480
Number of pages34
JournalMathematics and Financial Economics
Volume16
Issue number3
Early online date28 Mar 2022
Publication statusPublished - Jul 2022

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.

Keywords

    q-fin.MF, math.PR, q-fin.RM, Consistent risk measures, Nonconvex Choquet integrals, Law invariance, Optimisation problems, Quasiconvex functionals

ASJC Scopus subject areas

Cite this

Law-Invariant Functionals that Collapse to the Mean: Beyond Convexity. / Liebrich, Felix-Benedikt; Munari, Cosimo.
In: Mathematics and Financial Economics, Vol. 16, No. 3, 07.2022, p. 447-480.

Research output: Contribution to journalArticleResearchpeer review

Liebrich FB, Munari C. Law-Invariant Functionals that Collapse to the Mean: Beyond Convexity. Mathematics and Financial Economics. 2022 Jul;16(3):447-480. Epub 2022 Mar 28. doi: 10.1007/s11579-022-00313-9
Liebrich, Felix-Benedikt ; Munari, Cosimo. / Law-Invariant Functionals that Collapse to the Mean : Beyond Convexity. In: Mathematics and Financial Economics. 2022 ; Vol. 16, No. 3. pp. 447-480.
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