Haezendonck-Goovaerts Capital Allocation Rules

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 secondly a more general one based on the, here introduced, concept of linking functions. Further on, we use the same construction of to extend the CARs previously introduced to HG risk measures. We therefore study the properties of different CARs for HG risk measures, both in the quantile-based setting and in the linking one. Finally, we provide robust versions of the introduced CARs, both considering the case of ambiguity over the probabilistic model and the one of multiple Young functions, following the scheme of.