On the Haezendonck-Goovaerts risk measure for extreme risks

► We are interested in the calculation of the Haezendonck-Goovaerts risk measure. ► The focus is on the case with an extreme value risk and a power Young function. ► We derive exact asymptotics for the Haezendonck-Goovaerts risk measure. ► We also consider the case with an exponential risk and a general Young function. ► Each result is examined numerically.