Frequency-Severity Experience Rating based on Latent Markovian Risk Profiles

TL;DR

This paper introduces a dynamic, latent Markovian risk profile model for insurance experience rating that captures frequency-severity dependence and updates customer risk assessments over time.

Contribution

It proposes a novel joint rating approach using Hidden Markov Models to model evolving risk profiles and claim behaviors, improving risk differentiation.

Findings

Identifies distinct customer risk profiles in auto insurance data.

Demonstrates improved risk premium calculation with dynamic profiles.

Shows the model captures frequency-severity dependence effectively.

Abstract

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.