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.
Bibliographical noteFunding Information:
This research was supported by Basic Science Research Program of the National Research Foundation of Korea ( 2012-8-0666 for Jeon; 2012-8-1657 for Kim) funded by the Korean government. The authors are grateful to the reviewers for helpful comments and suggestions.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Economics and Econometrics
- Statistics, Probability and Uncertainty