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

摘要

The Haezendonck-Goovaerts risk measure is based on the premium calculation principle induced by an Orlicz norm, which is defined via an increasing and convex Young function and a parameter q ∈ (0,1) representing the confidence level. In this paper, we first reestablish the first-order expansions of the Haezendonck-Goovaerts risk measure for extreme risks with a power Young function in Tang and Yang (2012) in terms of the tail quantile function. Second, we are interested in the calculation of the second-order expansions of the Haezendonck-Goovaerts risk measure as q ↑ 1- We only consider the case in which the risk variable belongs to the max-domain of attraction of an extreme value distribution.