Credibility in Loss Reserving

This article proposes using credibility theory in the context of stochastic claims reserving. We consider the situation where an insurer has access to the claims experience of its peer competitors and has the potential to improve prediction of outstanding liabilities by incorporating information from other insurers. Based on the framework of Bayesian linear models, we show that the development factor in the classical chain-ladder setting has a credibility expression, i.e. a weighted average of the prior mean and the best estimate from the data. In the empirical analysis, we examine loss triangles for the line of commercial auto insurance from a portfolio of insurers in the US. We employ hierarchical model for the specification of prior and show that prediction could be improved through borrowing strength among insurers based on a hold-out sample validation.

Keywords: Bayesian Modeling, Chain-ladder method, Hierarchical model