In insurance and finance it is often important to have a satisfactory estimate for an extreme quantile, like the one underlying capital requirements in Solvency II and Basel III. If credibility techniques on means are used for the determination of such quantiles, this can lead to quite unsatisfactory results, in particular in the presence of outliers in the data. Quantile credibility models themselves, however, cannot perform effectively when the set of data has a nested (hierarchical) structure. This paper develops multi-stage nested classification hierarchical credibility models for quantiles as an alternative to Jewell’s (G Ist Ital Attuari 38:1–16, 1975) approach, where more than one risk factor divides the portfolio into different sectors or classes. We establish hierarchical quantile credibility estimators and illustrate their performance in two numerical illustrations.

中文翻译：

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多阶段嵌套分类可信度模型中的分位数

在保险和金融领域，对极端分位数进行令人满意的估算通常很重要，例如，偿付能力标准II和巴塞尔协议III中的一项基本资本要求。如果使用均值的可信度技术来确定此类分位数，则可能导致相当不令人满意的结果，尤其是在数据中存在异常值的情况下。但是，当数据集具有嵌套（分层）结构时，分位数可信度模型本身无法有效执行。本文开发了针对分位数的多阶段嵌套分类等级可信度模型，以替代Jewell（G Ist Ital Attuari 38：1–16，1975）方法，该方法将多个投资组合划分为不同的部门或类别。