## Credibility theory based on trimming.(English)Zbl 1284.91245

Summary: 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.

### MSC:

 91B30 Risk theory, insurance (MSC2010)

### Keywords:

credibility; trimmed mean; L-estimator; risk measure
Full Text:

### References:

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