A Population Sampling Framework for Claim Reserving in General Insurance

TL;DR

This paper presents a unified statistical framework for claim reserving in insurance, integrating macro- and micro-level models through population sampling theory to improve accuracy and address sampling bias.

Contribution

It introduces a novel unified framework based on population sampling theory that combines aggregate and individual claim models for better reserving accuracy.

Findings

Unified framework improves reserve estimation accuracy.

Addresses sampling bias with advanced statistical methods.

Demonstrates practical benefits using Canadian auto insurance data.

Abstract

Claim reserving in insurance has been studied through two primary frameworks: the macro-level approach, which estimates reserves at an aggregate level (e.g., Chain-Ladder), and the micro-level approach, which estimates reserves at the individual claim level Antonio and Plat (2014). These frameworks are based on fundamentally different theoretical foundations, creating a degree of incompatibility that limits the adoption of more flexible models. This paper introduces a unified statistical framework for claim reserving, grounded in population sampling theory. We show that macro- and micro-level models represent extreme yet natural cases of an augmented inverse probability weighting (AIPW) estimator. This formulation allows for a seamless integration of principles from both aggregate and individual models, enabling more accurate and flexible estimations. Moreover, this paper also addresses critical issues of sampling bias arising from partially observed claims data-an often overlooked challenge in insurance. By adapting advanced statistical methods from the sampling literature, such as double-robust estimators, weighted estimating equations, and synthetic data generation, we improve predictive accuracy and expand the tools available for actuaries. The framework is illustrated using Canadian auto insurance data, highlighting the practical benefits of the sampling-based methods.