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 (Bellini and Rosazza Gianin, 2008; Goovaerts et al., 2004). To this aim, we generalize the capital allocation rule (CAR) introduced by Xun et al. (2019) for Orlicz risk premia (Haezendonck and Goovaerts, 1982) as well as for HG risk measures, using an approach based on Orlicz quantiles (Bellini and Rosazza Gianin, 2012). We therefore study the properties of different CARs for HG risk measures in the quantile-based setting. Finally, we provide robust versions of the introduced CARs, considering ambiguity both over the probabilistic model and over the Young function, following the scheme of Bellini et al. (2018).