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