Risk-Adjusted Estimation and Graduation of Transition Intensities for Disability and Long-Term Care Insurance: A Multi-State Model Approach

This paper introduces a methodology for estimating transition intensities in a multi-state model for disability and long-term care insurance. We propose a novel framework that integrates observable risk factors, such as demographic (age and sex), lifestyle (smoking and exercise habits) and health-related variables (body mass index), into the estimation and graduation of transition intensities, using a parametric approach based on the Gompertz–Makeham law and generalised linear models. The model features four states—autonomous, dead, and two intermediate states representing varying disability levels—providing a detailed view of disability/lack of autonomy progression. To illustrate the proposed framework, we simulate a dataset with individual risk profiles and model trajectories, mirroring Portugal’s demographic composition. This allows us to derive a functional form (as a function of age) for the transition intensities, stratified by relevant risk factors, thus enabling precise risk differentiation. The results offer a robust basis for developing tailored pricing structures in the Portuguese market, with broader applications in actuarial science and insurance. By combining granular disability modelling with risk factor integration, our approach enhances accuracy in pricing structure and risk assessment.