Fair Pricing in Long-Term Insurance: A Unified Framework

Extant literature on fair pricing methods for actuarial contexts has primarily focused on the regression setting. While such approaches are well-suited to short-term
products, it is unclear how they generalize to long-term products, whose pricing essentially relies on estimating transition rates in multi-state models. To address this gap,
we propose a unified framework that recasts the estimation of any given multi-state
transition model as a set of Poisson regression problems. This reformulation enables
the direct application of existing fair pricing methods, which together constitute our
proposed methodology. As an illustration, we apply the framework to a fair pricing
exercise for a stylized long-term care insurance product using data from the University
of Michigan Health and Retirement Study (HRS), focusing on a post-processing approach. We further explain how the framework readily accommodates pre-processing
and in-processing fairness methods.