The Haezendonck-Goovaerts (H-G) risk measure, proposed by Haezendonck & Goovaerts [(1982). A new premium calculation principle based on Orlicz norms. Insurance: Mathematics and Economics 1(1), 41–53], has attracted much attention in the fields of finance, insurance and quantitative risk management in recent years. In this paper, we focus on the study of efficient estimators for the H-G risk measure. We first propose a new estimator for the H-G risk measure with a power Young function based on its first-order expansion at intermediate levels, and then we extend it to extreme levels under the second-order regular variation condition by using extreme value theory. Asymptotic normality is established for both the intermediate- and extreme-level estimators. We also propose an estimator for the H-G risk measure with a general Young function and establish its consistency. Numerical simulations are conducted to show that the performances of the proposed estimators are quite good and their computation processes are easy, thereby making the H-G risk measure highly efficient for practical applications. An analysis of real data is also provided.

Haezendonck-Goovaerts (HG) 风险度量，由 Haezendonck & Goovaerts [(1982) 提出。基于 Orlicz 规范的新保费计算原则。保险：数学和经济学 1(1), 41-53]，近年来在金融、保险和量化风险管理领域备受关注。在本文中，我们重点研究 HG 风险测度的有效估计量。我们首先基于 HG 风险度量在中间级别的一阶展开提出了一个具有幂 Young 函数的新估计量，然后我们通过使用极值理论将其扩展到二阶规则变化条件下的极端级别。为中间和极端水平的估计量建立了渐近正态性。我们还提出了具有一般 Young 函数的 HG 风险度量的估计器并建立其一致性。数值模拟表明，所提出的估计器的性能相当好，计算过程简单，从而使 HG 风险度量对于实际应用非常有效。还提供了对真实数据的分析。