  Loss development modelling is the actuarial practice of predicting the total
'ultimate' losses incurred on a set of policies once all claims are reported
and settled. This poses a challenging prediction task as losses frequently take
years to fully emerge from reported claims, and not all claims might yet be
reported. Loss development models frequently estimate a set of 'link ratios'
from insurance loss triangles, which are multiplicative factors transforming
losses at one time point to ultimate. However, link ratios estimated using
classical methods typically underestimate ultimate losses and cannot be
extrapolated outside the domains of the triangle, requiring extension by 'tail
factors' from another model. Although flexible, this two-step process relies on
subjective decision points that might bias inference. Methods that jointly
estimate 'body' link ratios and smooth tail factors offer an attractive
alternative. This paper proposes a novel application of Bayesian hidden Markov
models to loss development modelling, where discrete, latent states
representing body and tail processes are automatically learned from the data.
The hidden Markov development model is found to perform comparably to, and
frequently better than, the two-step approach on numerical examples and
industry datasets.
