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Contribution Details

Type Journal Article
Scope Discipline-based scholarship
Title Law-invariant functionals that collapse to the mean
Organization Unit
Authors
  • Fabio Bellini
  • Pablo Koch Medina
  • Cosimo Munari
  • Gregor Svindland
Item Subtype Original Work
Refereed Yes
Status Published in final form
Language
  • English
Journal Title Insurance: Mathematics and Economics
Geographical Reach international
ISSN 0167-6687
Volume 98
Page Range 83 - 91
Date 2021
Abstract Text 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.
Free access at Official URL
Official URL https://www.sciencedirect.com/science/article/pii/S0167668721000354
Digital Object Identifier 10.1016/j.insmatheco.2021.03.002
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