Pareto optimal allocations and optimal risk sharing for coherent or convex risk measures as well as for insurance prices have been studied widely in the literature. In particular, Pareto optimal allocations have been characterized by applying inf-convolution of risk measures and convex...

We introduce the definition of set-valued capital allocation rule, in the context of set- valued risk measures. In analogy to some well known methods for the scalar case based on the idea of marginal contribution and hence on the notion of gradient and sub-gradient of a risk measure, and under...

We introduce the notion of set-valued Capital Allocation rule, and study Capital allocation principles for multivariate set-valued coherent and convex risk measures. We compare these rules with some of those mostly used for univariate (single-valued) risk measures

This paper deals with the problem of capital allocation for a peculiar class of risk measures, namely the Haezendonck-Goovaerts (HG) ones. We generalize the capital allocation rule (CAR) introduced by Xun et al. for Orlicz risk premia, using firstly an approach based on Orlicz quantiles and...

This paper introduces a new approach to face capital allocation problems from the perspective of acceptance sets, by defining the family of sub-acceptance sets. We study the relations between the notions of sub-acceptability and acceptability of a risky position as well as their impact on...

In the context of capital allocation principles for (not necessarily coherent) risk measures, we derive - under mild conditions - some representation results as ``collapse to the mean'' in a generalized sense. This approach is related to the well-known Gradient allocation and allows to extend a...