Frequency-Severity Experience Rating based on Latent Markovian Risk Profiles
This work addresses the need for more accurate risk assessment in automobile insurance by accounting for frequency-severity dependence, though it is incremental as it builds on existing credibility theory with a novel modeling twist.
The authors tackled the problem of traditional Bonus-Malus Systems ignoring the dependence between claim counts and sizes by proposing a joint experience rating approach using latent Markovian risk profiles, which was applied to a Dutch automobile insurance portfolio to better distinguish customer risks.
Bonus-Malus Systems traditionally consider a customer's number of claims irrespective of their sizes, even though these components are dependent in practice. We propose a novel joint experience rating approach based on latent Markovian risk profiles to allow for a positive or negative individual frequency-severity dependence. The latent profiles evolve over time in a Hidden Markov Model to capture updates in a customer's claims experience, making claim counts and sizes conditionally independent. We show that the resulting risk premia lead to a dynamic, claims experience-weighted mixture of standard credibility premia. The proposed approach is applied to a Dutch automobile insurance portfolio and identifies customer risk profiles with distinctive claiming behavior. These profiles, in turn, enable us to better distinguish between customer risks.