Björn Löfdahl Grelsson: Disability insurance: Hidden Markov models and claims reserving

Abstract: A popular approach to estimating population transition rates, including mortality and disability, is the Lee-Carter model. It relies on a two-step method involving parameter estimation from historical data and subsequent calibration of a time series model. This approach may in fact lead to both conceptual and numerical problems since any time trend components of the model are incoherently treated as both model parameters and realizations of a stochastic process. We suggest that this general two-step approach can be improved in the following way: First, we assume a stochastic process form for the time trend component. The corresponding transition densities are then incorporated into the likelihood, and the model parameters are estimated using the Expectation-Maximization algorithm. We illustrate the modelling procedure by fitting the model to Swedish disability claims data. Further, we show how the results may be used for claims reserving for standard disability policies.