Second-order properties of the Haezendonck-Goovaerts risk measure for extreme risks

► We reestablish the first-order approximations of the Haezendonck-Goovaerts risk measure in Tang and Yang (2012). ► We obtain the second-order approximations of the Haezendonck-Goovaerts risk measure. ► We only consider the case in which the risk variable belongs to a max-domain of attraction of the extreme distributions.