Details
| Original language | English |
|---|---|
| Pages (from-to) | 83-91 |
| Number of pages | 9 |
| Journal | Insurance: Mathematics and Economics |
| Volume | 98 |
| Early online date | 17 Mar 2021 |
| Publication status | Published - May 2021 |
Abstract
We discuss when law-invariant convex functionals “collapse to the mean”. More precisely, we show that, in a large class of spaces of random variables and under mild semicontinuity assumptions, the expectation functional is, up to an affine transformation, the only law-invariant convex functional that is linear along the direction of a nonconstant random variable with nonzero expectation. This extends results obtained in the literature in a bounded setting and under additional assumptions on the functionals. We illustrate the implications of our general results for pricing rules and risk measures.
Keywords
- Affinity, Law invariance, Pricing rules, Risk measures, Translation invariance
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Economics, Econometrics and Finance(all)
- Economics and Econometrics
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Insurance: Mathematics and Economics, Vol. 98, 05.2021, p. 83-91.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Law-invariant functionals that collapse to the mean
AU - Bellini, Fabio
AU - Koch-Medina, Pablo
AU - Munari, Cosimo
AU - Svindland, Gregor
N1 - Funding Information: Partial support through the SNF, Switzerland project 100018-189191 ?Value Maximizing Insurance Companies: An Empirical Analysis of the Cost of Capital and Investment Policies? is gratefully acknowledged.
PY - 2021/5
Y1 - 2021/5
N2 - We discuss when law-invariant convex functionals “collapse to the mean”. More precisely, we show that, in a large class of spaces of random variables and under mild semicontinuity assumptions, the expectation functional is, up to an affine transformation, the only law-invariant convex functional that is linear along the direction of a nonconstant random variable with nonzero expectation. This extends results obtained in the literature in a bounded setting and under additional assumptions on the functionals. We illustrate the implications of our general results for pricing rules and risk measures.
AB - We discuss when law-invariant convex functionals “collapse to the mean”. More precisely, we show that, in a large class of spaces of random variables and under mild semicontinuity assumptions, the expectation functional is, up to an affine transformation, the only law-invariant convex functional that is linear along the direction of a nonconstant random variable with nonzero expectation. This extends results obtained in the literature in a bounded setting and under additional assumptions on the functionals. We illustrate the implications of our general results for pricing rules and risk measures.
KW - Affinity
KW - Law invariance
KW - Pricing rules
KW - Risk measures
KW - Translation invariance
UR - http://www.scopus.com/inward/record.url?scp=85102802701&partnerID=8YFLogxK
U2 - 10.1016/j.insmatheco.2021.03.002
DO - 10.1016/j.insmatheco.2021.03.002
M3 - Article
AN - SCOPUS:85102802701
VL - 98
SP - 83
EP - 91
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
SN - 0167-6687
ER -