On the Haezendonck-Goovaerts risk measure for extreme risks

摘要

In this paper, we are interested in the calculation of the Haezendonck-Goovaerts risk measure, which is defined via a convex Young function and a parameter q(€) (0,1) representing the confidence level. We mainly focus on the case in which the risk variable follows a distribution function from a max-domain of attraction. For this case, we restrict the Young function to be a power function and we derive exact asymptotics for the Haezendonck-Goovaerts risk measure as q ↑ 1. As a subsidiary, we also consider the case with an exponentially distributed risk variable and a general Young function, and we obtain an analytical expression for the Haezendonck-Goovaerts risk measure.