This paper makes the point on a well known property of capital allocation rules, namely the one called no-undercut. Its desirability in capital allocation stems from some stability game theoretical features that are related to the notion of core, both for finite and infinite games. We review these aspects, by relating them to the properties of the risk measures that are involved in capital allocation problems. We also discuss some problems and possible extensions that arise when we deal with non-coherent risk measures.

In this paper, we focus on capital allocation methods based on marginal contributions. In particular, concerning the relation between linear capital allocation rules and the well-known Gradient (or Euler) allocation, we investigate an extension to the convex and non-differentiable case of the result above and its link with the “generalized collapse to the mean” problem. This preliminary result goes in the direction of applying the popular marginal contribution method, which fosters the diversification of risk, to the case of more general risk measures. In this context, we will also discuss and point out some numerical issues linked to marginal methods and some future research directions.