Details
| Original language | English |
|---|---|
| Pages (from-to) | 447-480 |
| Number of pages | 34 |
| Journal | Mathematics and Financial Economics |
| Volume | 16 |
| Issue number | 3 |
| Early online date | 28 Mar 2022 |
| Publication status | Published - Jul 2022 |
Abstract
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
- Economics, Econometrics and Finance(all)
- Finance
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Mathematics and Financial Economics, Vol. 16, No. 3, 07.2022, p. 447-480.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Law-Invariant Functionals that Collapse to the Mean
T2 - Beyond Convexity
AU - Liebrich, Felix-Benedikt
AU - Munari, Cosimo
N1 - Funding Information: We would like to thank two anonymous referees, the Editor, the participants of the Weekly Seminars on Risk Management and Actuarial Science at the University of Waterloo and of the Mathematical Finance Seminar at the University of Bielefeld, and Ruodu Wang for their valuable input which helped improving earlier versions of this manuscript. Data sharing not applicable to this article as no datasets were generated or analysed during the current study.
PY - 2022/7
Y1 - 2022/7
N2 - 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.
AB - 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.
KW - q-fin.MF
KW - math.PR
KW - q-fin.RM
KW - Consistent risk measures
KW - Nonconvex Choquet integrals
KW - Law invariance
KW - Optimisation problems
KW - Quasiconvex functionals
UR - http://www.scopus.com/inward/record.url?scp=85127302611&partnerID=8YFLogxK
U2 - 10.1007/s11579-022-00313-9
DO - 10.1007/s11579-022-00313-9
M3 - Article
VL - 16
SP - 447
EP - 480
JO - Mathematics and Financial Economics
JF - Mathematics and Financial Economics
SN - 1862-9679
IS - 3
ER -