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.