Modeling Heterogeneity and Serial Correlation of Non-Life Insurance Policyholders Using a GLM–HMM Framework

This study proposes a GLM modulated by a discrete-time Hidden Markov Model (HMM) for modeling claims in non-life insurance. The model is based on the integrated use of HMM and GLM under a longitudinal data structure. Each hidden state represents a risk regime defined by its own GLM parameters. Transitions between states are considered under three assumptions: homogeneous, heterogeneous, and autoregressive heterogeneous structures. These assumptions allow for the modeling of hidden states using observable risk factors and past claim frequencies. Thus, the GLM-HMM allows for the integrated evaluation of unobservable heterogeneity, the impact of observed risk factors, and the indirect effect of past claim observations (serial correlation) on transitions between states. Parameter estimation is performed using the Baum–Welch algorithm. The performance of the estimation procedure is examined using simulation-based datasets. Additionally, a five-year longitudinal portfolio of motor insurance is analyzed. GLM, GLMM, ZIP, and GLM-HMM models are estimated using data from the first four years. Net premiums and expected claims costs were compared for the fifth year. The findings demonstrate that the GLM-HMM model better accommodates hidden states to risk changes. This model provides a practical and interpretable structure from an actuarial pricing perspective. The GLM-HMM approach differs from static models and continuous random effects models. It represents hidden states in claims data in a clear and consistent manner. In this respect, the study offers a flexible and applicable framework for dynamic risk classification.