Fair Pricing in Long-Term Insurance: A Unified Framework

TL;DR

This paper addresses fair pricing for long-term insurance by reframing multi-state transition estimation as a set of Poisson regressions, enabling the transfer of short-term fair-pricing methods to long-term contexts. It introduces a unified Poisson-survival framework where transition intensities $\lambda_{k,m}(x)$ are modeled via $\ln \lambda_{k,m}(x)= f_m(\mathbf{z}_k, x)$ and estimated with exposure-adjusted Poisson likelihoods, while preserving actuarial practice. The LTCI case study using HRS data demonstrates three pricing settings—best-estimate, race-blind, and fairness-adjusted via post-processing—showing that post-processing can reduce proxy discrimination across racial groups. The paper also outlines pre-processing and in-processing illustrations (optimal transport and adversarial debiasing) to extend fairness to long-term pricing, highlighting both practical benefits and limitations. Overall, the framework provides a coherent, adaptable path to fair pricing for long-horizon insurance products and motivates further research into multi-state fairness across diverse products and regulatory regimes.

Abstract

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.

Figures (5)

• Figure 1: Multi-state transition models. Note: Panel (a) depicts the two-state model for pricing life insurance and annuity products. Panel (b) depicts a three-state model with recovery from disability.
• Figure 2: The adversarial learning framework of beutel2017data. Note: $W = f(\mathbf{Z})$ refers to the trained representation, whereas $f$, $g$ and $h$ are functions learned by the network.
• Figure 3: Lump-sum premiums by racial group. Note: Each panel represents a different modeling assumption, as indicated by the panel title. There are three smoothed lines in each panel, one for each racial group. Each smoothed line is generated using a generalized additive model (GAM), regressing the lump-sum premium on age. The gray band represents the 95% confidence interval of the GAM.
• Figure 4: Adversarial learning framework tailored to long-term insurance, adapted from beutel2017data. Note: $\mathbf{Z}$ and $x$ refer to the non-age covariates and age, respectively; $W=f(\mathbf{Z})$ is the trained representation, and functions $f$, $h$ and $g_1, \ldots, g_M$ are functions learned by the network.
• Figure D.1: A version of the adversarial learning framework tailored to long-term insurance, adapted from beutel2017data using the divide-and-conquer approach, shown for transition $m$. Note: $\mathbf{Z}$ and $x$ refer to the non-age covariates and age, respectively; $W_m=f_m(\mathbf{Z})$ is the trained representation, and functions $f_m$, $g_m$ and $h_m$ are functions learned by the network.