Law-invariant functionals that collapse to the mean

@article{Bellini2020LawinvariantFT,
  title={Law-invariant functionals that collapse to the mean},
  author={Fabio Bellini and Pablo Koch-Medina and Cosimo Munari and Gregor Svindland},
  journal={arXiv: Mathematical Finance},
  year={2020}
}
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… Expand
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