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Law-invariant functionals that collapse to the mean


Bellini, Fabio; Koch-Medina, Pablo; Munari, Cosimo; Svindland, Gregor (2021). Law-invariant functionals that collapse to the mean. Insurance: Mathematics and Economics, 98:83-91.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Economics and Econometrics
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Scope:Discipline-based scholarship (basic research)
Language:English
Date:May 2021
Deposited On:02 Sep 2021 05:18
Last Modified:26 May 2024 01:43
Publisher:Elsevier
ISSN:0167-6687
OA Status:Hybrid
Free access at:Official URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/j.insmatheco.2021.03.002
Official URL:https://www.sciencedirect.com/science/article/pii/S0167668721000354
Other Identification Number:merlin-id:20872
  • Content: Published Version
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)