Haezendonck-Goovaerts risk measures and Orlicz quantiles

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• 作者：Fabio Bellini ^{fabio.bellini@unimib.it} ; Emanuela Rosazza Gianin ; ^{emanuela.rosazza1@unimib.it}
• 关键词：IM30 ; IE13
• 刊名：Insurance ; Mathematics and Economics
• 出版年：2012
• 期刊代码：25_01676687
• 类别：mt
• 出版时间：July, 2012
• 卷：51
• 期：1
• 页码：107-114
• 文件大小：263 K

摘要

In this paper, we study the well-known Haezendonck-Goovaerts risk measures on their natural domain, that is on Orlicz spaces and, in particular, on Orlicz hearts. We provide a dual representation as well as the optimal scenario in such a representation and investigate the properties of the minimizer (that we call Orlicz quantile) in the definition of the Haezendonck-Goovaerts risk measure. Since Orlicz quantiles fail to satisfy an internality property, bilateral Orlicz quantiles are also introduced and analyzed.