Conformal prediction for frequency-severity modeling

2023-07-24

arXiv.org

AI Summary

To address the lack of statistical guarantees for prediction intervals under limited samples in insurance claims forecasting, this paper proposes the first model-agnostic conformal prediction framework tailored for frequency-severity two-stage modeling. Methodologically, it innovatively extends split conformal prediction to joint modeling settings and replaces conventional hold-out calibration sets with out-of-bag (OOB) estimates from random forests, thereby eliminating reliance on independent calibration data. The approach integrates parametric statistical models with machine learning, balancing interpretability and flexibility. Experiments on both synthetic and real-world insurance datasets demonstrate that the framework significantly improves prediction interval coverage while rigorously maintaining finite-sample statistical validity and robustness. This work establishes a new paradigm for actuarial modeling that unifies theoretical rigor with practical feasibility.

Abstract

We present a model-agnostic framework for the construction of prediction intervals of insurance claims, with finite sample statistical guarantees, extending the technique of split conformal prediction to the domain of two-stage frequency-severity modeling. The framework effectiveness is showcased with simulated and real datasets using classical parametric models and contemporary machine learning methods. When the underlying severity model is a random forest, we extend the two-stage split conformal prediction algorithm, showing how the out-of-bag mechanism can be leveraged to eliminate the need for a calibration set in the conformal procedure.

Problem

• Construct prediction intervals for insurance claims
• Extend conformal prediction to frequency-severity modeling
• Leverage out-of-bag mechanism to avoid calibration sets

Innovation

• Model-agnostic framework for prediction intervals
• Extends split conformal prediction to two-stage modeling
• Leverages out-of-bag mechanism for random forest