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.

💡 Research Summary

The paper addresses a critical gap in actuarial science: the lack of fair pricing methods for long‑term insurance products, whose premiums are derived from multi‑state transition rates rather than a single loss outcome. The authors propose a unified framework that recasts the estimation of any multi‑state transition model as a series of Poisson regression problems. By treating transition counts as the response variable and exposure time as an offset, each transition intensity λ can be modeled with a log‑linear specification and estimated via standard Poisson GLM techniques. This reformulation bridges the methodological divide between short‑term regression‑based fair pricing approaches and the actuarial calculations required for long‑term policies.

Building on this representation, the paper shows how three families of fairness adjustments—pre‑processing, in‑processing, and post‑processing—can be seamlessly integrated. Pre‑processing may involve optimal‑transport re‑weighting of the transition data to achieve demographic parity before model fitting. In‑processing adds fairness‑related penalty terms (e.g., the discrimination‑free premium formulation of Lindholm et al.) directly to the Poisson likelihood, encouraging estimated intensities to be independent of protected attributes. Post‑processing adjusts the fitted intensities or the resulting premiums to satisfy group fairness criteria such as demographic parity.

The authors illustrate the framework with a stylized long‑term care insurance (LTCI) case study using the University of Michigan Health and Retirement Study (HRS). A three‑state model (healthy, disabled, dead) is specified; separate Poisson regressions are fitted for each of the four possible transitions. After fitting, a post‑processing step equalizes the transition intensities across sensitive groups, and the adjusted intensities are propagated through Chapman‑Kolmogorov equations to obtain multi‑year transition probabilities. These probabilities are then inserted into expected present value (EPV) formulas for premiums and benefits, yielding fair‑adjusted LTCI premiums. The empirical results quantify how fairness adjustments at the transition level translate into changes in final premiums, demonstrating the practical impact of the proposed methodology.

Key contributions include: (1) a methodological proof that any multi‑state model can be expressed as Poisson regressions, providing a transparent statistical backbone for long‑term pricing; (2) a conceptual bridge that allows existing short‑term fair pricing techniques to be applied without redesigning the underlying actuarial model; (3) a practical demonstration that fairness can be enforced at the transition stage and reflected in actuarially fair premiums. The work offers regulators and practitioners a systematic tool for ensuring algorithmic fairness in long‑term insurance, especially in jurisdictions that now require scrutiny of external consumer data used in underwriting.