Law-invariant functionals that collapse to the mean

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • Fabio Bellini
  • Pablo Koch-Medina
  • Cosimo Munari
  • Gregor Svindland

Externe Organisationen

  • University of Milano-Bicocca
  • Universität Zürich (UZH)
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)83-91
Seitenumfang9
FachzeitschriftInsurance: Mathematics and Economics
Jahrgang98
Frühes Online-Datum17 März 2021
PublikationsstatusVeröffentlicht - Mai 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.

ASJC Scopus Sachgebiete

Zitieren

Law-invariant functionals that collapse to the mean. / Bellini, Fabio; Koch-Medina, Pablo; Munari, Cosimo et al.
in: Insurance: Mathematics and Economics, Jahrgang 98, 05.2021, S. 83-91.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Bellini F, Koch-Medina P, Munari C, Svindland G. Law-invariant functionals that collapse to the mean. Insurance: Mathematics and Economics. 2021 Mai;98:83-91. Epub 2021 Mär 17. doi: 10.1016/j.insmatheco.2021.03.002
Bellini, Fabio ; Koch-Medina, Pablo ; Munari, Cosimo et al. / Law-invariant functionals that collapse to the mean. in: Insurance: Mathematics and Economics. 2021 ; Jahrgang 98. S. 83-91.
Download
@article{fcc381263e014a6db4369b86361fcf7b,
title = "Law-invariant functionals that collapse to the mean",
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",
author = "Fabio Bellini and Pablo Koch-Medina and Cosimo Munari and Gregor Svindland",
note = "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. ",
year = "2021",
month = may,
doi = "10.1016/j.insmatheco.2021.03.002",
language = "English",
volume = "98",
pages = "83--91",
journal = "Insurance: Mathematics and Economics",
issn = "0167-6687",
publisher = "Elsevier",

}

Download

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 -