Quantiles in a multi-stage nested classification credibility model

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.