Details
| Original language | English |
|---|---|
| Pages (from-to) | 318-341 |
| Number of pages | 24 |
| Journal | SIAM Journal on Financial Mathematics |
| Volume | 12 |
| Issue number | 1 |
| Publication status | Published - 4 Mar 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.
Keywords
- Dilation monotonicity, Extension results, Infimal convolutions, Kusuoka representations, Law invariance, Quantile representations, Schur convexity
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Economics, Econometrics and Finance(all)
- Finance
- Mathematics(all)
- Applied Mathematics
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In: SIAM Journal on Financial Mathematics, Vol. 12, No. 1, 04.03.2021, p. 318-341.
Research output: Contribution to journal › Article › Research › 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 -