Publication: Law-invariant functionals that collapse to the mean
Law-invariant functionals that collapse to the mean
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Bellini, F., Koch-Medina, P., Munari, C., & Svindland, G. (2021). Law-invariant functionals that collapse to the mean. Insurance: Mathematics and Economics, 98, 83–91. https://doi.org/10.1016/j.insmatheco.2021.03.002
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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 implicati
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- Bellini, Fabio
- Munari, Cosimo
- Svindland, Gregor
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Bellini, F., Koch-Medina, P., Munari, C., & Svindland, G. (2021). Law-invariant functionals that collapse to the mean. Insurance: Mathematics and Economics, 98, 83–91. https://doi.org/10.1016/j.insmatheco.2021.03.002
