Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 318-341 |
| Seitenumfang | 24 |
| Fachzeitschrift | SIAM Journal on Financial Mathematics |
| Jahrgang | 12 |
| Ausgabenummer | 1 |
| Publikationsstatus | Veröffentlicht - 4 März 2021 |
Abstract
We establish general versions of a variety of results for quasiconvex, lower-semicontinuous, and law-invariant functionals. Our results extend well-known results from the literature to a large class of spaces of random variables. We sometimes obtain sharper versions, even for the well-studied case of bounded random variables. Our approach builds on two fundamental structural results for law-invariant functionals: the equivalence of law invariance and Schur convexity, i.e., monotonicity with respect to the convex stochastic order, and the fact that a law-invariant functional is fully determined by its behavior on bounded random variables. We show how to apply these results to provide a unifying perspective on the literature on law-invariant functionals, with special emphasis on quantile-based representations, including Kusuoka representations, dilatation monotonicity, and infimal convolutions.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Numerische Mathematik
- Volkswirtschaftslehre, Ökonometrie und Finanzen (insg.)
- Finanzwesen
- Mathematik (insg.)
- Angewandte Mathematik
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in: SIAM Journal on Financial Mathematics, Jahrgang 12, Nr. 1, 04.03.2021, S. 318-341.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Law-invariant functionals on general spaces of random variables
AU - Bellini, Fabio
AU - Koch-Medina, Pablo
AU - Munari, Cosimo
AU - Svindland, Gregor
PY - 2021/3/4
Y1 - 2021/3/4
N2 - We establish general versions of a variety of results for quasiconvex, lower-semicontinuous, and law-invariant functionals. Our results extend well-known results from the literature to a large class of spaces of random variables. We sometimes obtain sharper versions, even for the well-studied case of bounded random variables. Our approach builds on two fundamental structural results for law-invariant functionals: the equivalence of law invariance and Schur convexity, i.e., monotonicity with respect to the convex stochastic order, and the fact that a law-invariant functional is fully determined by its behavior on bounded random variables. We show how to apply these results to provide a unifying perspective on the literature on law-invariant functionals, with special emphasis on quantile-based representations, including Kusuoka representations, dilatation monotonicity, and infimal convolutions.
AB - We establish general versions of a variety of results for quasiconvex, lower-semicontinuous, and law-invariant functionals. Our results extend well-known results from the literature to a large class of spaces of random variables. We sometimes obtain sharper versions, even for the well-studied case of bounded random variables. Our approach builds on two fundamental structural results for law-invariant functionals: the equivalence of law invariance and Schur convexity, i.e., monotonicity with respect to the convex stochastic order, and the fact that a law-invariant functional is fully determined by its behavior on bounded random variables. We show how to apply these results to provide a unifying perspective on the literature on law-invariant functionals, with special emphasis on quantile-based representations, including Kusuoka representations, dilatation monotonicity, and infimal convolutions.
KW - Dilation monotonicity
KW - Extension results
KW - Infimal convolutions
KW - Kusuoka representations
KW - Law invariance
KW - Quantile representations
KW - Schur convexity
UR - http://www.scopus.com/inward/record.url?scp=85102840971&partnerID=8YFLogxK
U2 - 10.1137/20M1341258
DO - 10.1137/20M1341258
M3 - Article
AN - SCOPUS:85102840971
VL - 12
SP - 318
EP - 341
JO - SIAM Journal on Financial Mathematics
JF - SIAM Journal on Financial Mathematics
SN - 1945-497X
IS - 1
ER -