101. Law-invariant functionals that collapse to the mean
- Author
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Bellini, F, Koch-Medina, P, Munari, C, Svindland, G, Bellini, Fabio, Koch-Medina, Pablo, Munari, Cosimo, Svindland, Gregor, Bellini, F, Koch-Medina, P, Munari, C, Svindland, G, Bellini, Fabio, Koch-Medina, Pablo, Munari, Cosimo, and Svindland, Gregor
- 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.
- Published
- 2021