Frequency-Severity Experience Rating based on Latent Markovian Risk Profiles

Bonus-Malus Systems (BMSs) are nowadays widely employed in automobile insurance to dynamically adjust a premium based on a customer's claims experience. The intuition behind these posterior ratemaking systems is that as we observe more claiming behavior, we learn more about the underlying risk profile. These systems are therefore a commercially attractive form of experience rating, in which we correct the prior premium for past claims to reflect our updated beliefs about a customer's risk profile. Moreover, they traditionally consider a customer's number of claims irrespective of their sizes and thus implicitly assume independence between the claim counts and sizes (Hey, 1970; Denuit et al., 2007; Boucher and Inoussa, 2014; Verschuren, 2021). Alternative Bayesian forms of experience rating typically depend only on the frequency component as well or consider the two components separately (see, e.g., Denuit and Lang (2004); Bühlmann and Gisler (2005); Mahmoudvand and Hassani (2009); Bermúdez and Karlis (2011, 2017)).