2020/09/09 by Bellini, Fabio, Koch-Medina, Pablo, Munari, Cosimo +1
#FOS: Economics and business #Mathematical Finance (q-fin.MF)
paper · doi:10.48550/arxiv.2009.04144
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.