Capital allocation à la Aumann–Shapley for non-differentiable risk measures

We study capital allocation rules satisfying suitable properties for convex and quasi-convex risk measures, by focusing in particular on a family of capital allocation rules based on the dual representation for risk measures and inspired by the Aumann–Shapley allocation principle. These rules extend some well known methods of capital allocation for coherent and convex risk measures to the case of non-Gateaux-differentiable risk measures. We also analyze the properties of the allocation principles here introduced and discuss their suitability in the quasi-convex context.