Risk measures in a quantile regression credibility framework with Fama/French data applications

In this paper we extend the idea of embedding the classical credibility model into risk measures, as was presented by Pitselis (2016), to the idea of embedding regression credibility into risk measures. The resulting credible regression risk measures capture the risk of individual insurer's contract (in finance, the individual asset return portfolio) as well as the portfolio risk consisting of several similar but not identical contracts (in finance, several similar portfolios of asset returns), which are grouped together to share the risk. In insurance, credibility plays a special role of spreading the risk. In financial terminology, credibility plays a special role of diversification of risk. For each model, regression credibility models are established and the robustness of these models is investigated. Applications to Fama/French financial portfolio data are also presented.