Credibility theory based on trimming

•In this paper we propose a credibility theory via truncation of the loss data.•The proposed framework contains the classical credibility theory as a special case.•It is shown that the trimmed mean is not a coherent risk measure.•Some related asymptotic properties are established.•A numerical illustration is provided.

The classical credibility theory proposed by Bühlmann has been widely used in general insurance applications. In this paper we propose a credibility theory via truncation of the loss data, or the trimmed mean. The proposed framework contains the classical credibility theory as a special case and is based on the idea of varying the trimming threshold level to investigate the sensitivity of the credibility premium. After showing that the trimmed mean is not a coherent risk measure, we investigate some related asymptotic properties of the structural parameters in credibility. Later a numerical illustration shows that the proposed credibility models can successfully capture the tail risk of the underlying loss model, thus providing a better landscape of the overall risk that insurers assume.