Claim Reserving via Inverse Probability Weighting: A Micro-Level Chain-Ladder Method

TL;DR

This paper enhances traditional macro-level claim reserving methods by integrating individual policyholder data through inverse probability weighting, providing a statistically grounded, flexible, and granular approach that bridges the gap between aggregate and micro-level models.

Contribution

It introduces a novel IPW-based framework that incorporates individual information into the Chain-Ladder method, establishing a solid statistical foundation for micro-level reserving.

Findings

Chain-Ladder is shown as a special case of the proposed IPW estimator.

The new method allows for granular, policyholder-level reserving with a population sampling basis.

The approach improves reserve prediction accuracy by leveraging individual data.

Abstract

Claim reserving primarily relies on macro-level models, with the Chain-Ladder method being the most widely adopted. These methods were heuristically developed without minimal statistical foundations, relying on oversimplified data assumptions and neglecting policyholder heterogeneity, often resulting in conservative reserve predictions. Micro-level reserving, utilizing stochastic modeling with granular information, can improve predictions but tends to involve less attractive and complex models for practitioners. This paper aims to strike a practical balance between aggregate and individual models by introducing a methodology that enables the Chain-Ladder method to incorporate individual information. We achieve this by proposing a novel framework, formulating the claim reserving problem within a population sampling context. We introduce a reserve estimator in a frequency and severity distribution-free manner that utilizes inverse probability weights (IPW) driven by individual information, akin to propensity scores. We demonstrate that the Chain-Ladder method emerges as a particular case of such an IPW estimator, thereby inheriting a statistically sound foundation based on population sampling theory that enables the use of granular information, and other extensions.