Experience Rating in Insurance

Abstract

These notes are part of the syllabus of statistical modeling in non-life insurance. Following the introductory classes on 'Non-Life Insurance: Mathematics & Statistics' and 'Data Analytics for Non-Life Insurance Pricing', these notes extend the fixed effects models to mixed effects models also integrating past claims history for insurance pricing. We study different approaches (a) fixed effects models not considering any past claims experience, (b) random effects models only considering past claims history, (c) mixed effects models combining fixed effects and random effects considerations. This can be achieved by either using static random effects models or dynamic random effects models. Generally, static random effects models are more easy to handle, however, they do not allow for a seniority weighting of past claims, in contrast to their dynamic counterparts. These models are complemented by machine learning approaches for experience rating, which mainly rely on network architectures that include an attention weight mechanism. All considered models are supported by data examples and code.

Keywords: Experience rating, posterior rating, bonus-malus systems, generalized linear models, neural networks, attention layer, Transformer, fixed effects models, random effects models, mixed effects models, panel data, cross-sectional data, credibility theory, Bayesian theory, insurance pricing, actuarial pricing

JEL Classification: G22