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

Tiantian Mao and Taizhong Hu

Insurance: Mathematics and Economics, 2012, vol. 51, issue 2, 333-343

Abstract: 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.

Keywords: (Extended) regular variation; Extreme value theory; First-order expansion; Max-domain attraction; Second-order expansion; Second-order regular variation; Young function (search for similar items in EconPapers)
JEL-codes: G22 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (15)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:51:y:2012:i:2:p:333-343

DOI: 10.1016/j.insmatheco.2012.06.003

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