We show that a law-invariant pricing functional defined on a general Orlicz space is typically incompatible with frictionless risky assets in the sense that one and only one of the following two alternatives hold: either every risky payoff has a strictly-positive bid-ask spread, or the pricing functional is given by an expectation and hence every payoff has zero bid-ask spread. In doing so we extend and unify a variety of “collapse to the mean” results from the literature such as those obtained in  and , and we highlight the key role played by law invariance in determining such a collapse. As a byproduct, we derive several applications to law-invariant acceptance sets, risk measures and Schur-convex functionals. Finally, we discuss the relevance of these results in the framework of market-consistent pricing of insurances, as outlined in .
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