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.