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.

Bellini, F., Koch-Medina, P., Munari, C., Svindland, G. (2021). Law-invariant functionals that collapse to the mean. INSURANCE MATHEMATICS & ECONOMICS, 98(May 2021), 83-91 [10.1016/j.insmatheco.2021.03.002].

Law-invariant functionals that collapse to the mean

Bellini, Fabio;
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.
Articolo in rivista - Articolo scientifico
Affinity; Law invariance; Pricing rules; Risk measures; Translation invariance;
English
17-mar-2021
2021
98
May 2021
83
91
none
Bellini, F., Koch-Medina, P., Munari, C., Svindland, G. (2021). Law-invariant functionals that collapse to the mean. INSURANCE MATHEMATICS & ECONOMICS, 98(May 2021), 83-91 [10.1016/j.insmatheco.2021.03.002].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/307876
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