Law-invariant functionals that collapse to the mean

Fabio Bellini, Pablo Koch-Medina, Cosimo Munari and Gregor Svindland

Insurance: Mathematics and Economics, 2021, vol. 98, issue C, 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.

Keywords: Law invariance; Affinity; Translation invariance; Pricing rules; Risk measures (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:98:y:2021:i:c:p:83-91

DOI: 10.1016/j.insmatheco.2021.03.002

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