Insurance Pricing Optimization via Off-Policy Evaluation

Fairness in insurance pricing remains a long-standing and deeply debated puzzle. On one hand, insurers, driven by profitability considerations, set premiums that differentiate across individual risks to achieve actuarial fairness. On the other hand, insurance serves a critical societal function by pooling risks across a population, motivating cross-subsidization among groups to promote solidarity fairness. The tension between these two competing notions of fairness makes insurance pricing inherently complex, particularly in modern settings where granular data allow for increasingly fine risk differentiation and regulators face growing pressure to protect vulnerable groups. To address this challenge, we propose an $α$-\textbf{F}air \textbf{I}ndividual \textbf{S}olvent \textbf{P}remium ($α$-FISP) framework for insurance pricing that explicitly captures the trade-off between actuarial and solidarity fairness while guaranteeing solvency, a fundamental requirement in insurance operations. We formulate the pricing problem as a constrained optimization task, where actuarially fair premiums are adjusted subject to budget constraints on cross-subsidization within each risk class. This formulation naturally yields a family of solutions parameterized by $α$, tracing a continuum between purely actuarial and purely solidarity-based pricing and enabling decision-makers to select an operating point along this fairness spectrum. We derive theoretical guarantees for the proposed framework. Numerical experiments show that $α$-FISP is computationally tractable and aligns well with the U.S. regulatory regimes featuring heterogeneous state-level fairness requirements.

We study offline inference for the optimal value in reinforcement learning under finite state and action spaces. Two new nuisances are derived as fixed points of a self-induced Bellman equation, in which we approximate the maximum Bellman operator by its softmax correspondence. We propose a debiased estimator through the Neyman orthogonality and establish its asymptotic normality under diverging horizons even when the behavior policy changes with time, as long as the nuisances have the statistical rates that can be achieved by many machine learning methods. We provide a concrete estimating procedure for these nuisances and show they can lead to valid inference. Synthetic experiments validate the numerical performance of our inference method, and we implement it in real-life decision-making problems, including bike repositioning and AI agentic tool use.

Resource-constrained pricing controllers can make fixed-price inference impossible: the controller's resource state may remove the target price neighborhood from the feasible set, even when every realized action has a known positive density. We formalize this support-exclusion failure through a local non-identification result and a realized information clock. We then design a target-aware pricing controller that certifies feasible target bands and logs continuous local densities. Localized debiasing gives studentized intervals whose width is governed by this clock. The resulting regret--information accounting, stated up to pilot re-solving error, shows that cheap exploration can be insufficient for inference: polynomial target mass gives polynomial rates, while a pure $1/t$ target branch does not yield shrinking fixed-target intervals without additional local movement. Experiments show calibration in certified bands and diagnostic abstention when the resource state collapses target support.