Law-Invariant Functionals that Collapse to the Mean: Beyond Convexity

Abstract We establish general “collapse to the mean” principles that provide conditions under which a law-invariant functional reduces an expectation. In convex setting, we retrieve and sharpen known results from literature. However, our also apply beyond setting. illustrate this by providing complete account of for quasiconvex functionals. special cases consistent risk measures Choquet integrals, can even dispense with quasiconvexity. addition, relate study solutions broad class optimisation problems objectives appear in mathematical finance, insurance, economics. show corresponding quantile formulations studied literature are sometimes illegitimate require further analysis.