A new strategy for finite-sample valid prediction of future insurance claims in the regression setting

The extant insurance literature demonstrates a paucity of finite-sample valid prediction intervals of future insurance claims in the regression setting. To address this challenge, this article proposes a new strategy that converts a predictive method in the unsupervised iid (independent identically distributed) setting to a predictive method in the regression setting. In particular, it enables an actuary to obtain infinitely many finite-sample valid prediction intervals in the regression setting.

💡 Research Summary

The paper addresses a long‑standing gap in actuarial science: the lack of finite‑sample valid prediction intervals for future insurance claims when explanatory variables are available (the regression setting). Existing approaches fall into three categories. Parametric models rely on strong distributional assumptions and are vulnerable to model misspecification and the selection effect. Non‑parametric methods avoid misspecification but typically require tuning parameters, which re‑introduce a selection effect, and they only guarantee asymptotic validity. Model‑free methods such as decision trees or random forests sidestep both issues but still do not provide finite‑sample guarantees. Conformal prediction is the only known model‑free technique that can deliver finite‑sample validity, yet prior conformal methods for regression either require approximations that break the guarantee or are computationally infeasible.

The authors propose a novel “transformation‑based” strategy that bridges the gap between the unsupervised iid setting (where many finite‑sample valid conformal intervals exist) and the supervised regression setting. The key idea is to introduce an arbitrary, user‑chosen transformation function (h:\mathbb{R}^p\to\mathbb{R}) (subject to (h(x)\ge 0) for insurance claims) and rewrite the data‑generating equation \