Modeling Dependencies in Claims Reserving with GEE

TL;DR

This paper introduces the use of generalized estimating equations (GEE) for claims reserving, allowing for dependency modeling within claim data, which improves prediction accuracy over traditional methods assuming independence.

Contribution

It extends claims reserving models by incorporating dependencies through GEE, proposing correlation structures, model selection criteria, and a novel mean square error estimate.

Findings

GEE improves reserve predictions by modeling dependencies.

Correlation structures enhance model flexibility.

The method outperforms traditional GLM-based approaches.

Abstract

A common approach to the claims reserving problem is based on generalized linear models (GLM). Within this framework, the claims in different origin and development years are assumed to be independent variables. If this assumption is violated, the classical techniques may provide incorrect predictions of the claims reserves or even misleading estimates of the prediction error. In this article, the application of generalized estimating equations (GEE) for estimation of the claims reserves is shown. Claim triangles are handled as panel data, where claim amounts within the same accident year are dependent. Since the GEE allow to incorporate dependencies, various correlation structures are introduced and some practical recommendations are given. Model selection criteria within the GEE reserving method are proposed. Moreover, an estimate for the mean square error of prediction for the claims reserves is derived in a nonstandard way and its advantages are discussed. Real data examples are provided as an illustration of the potential benefits of the presented approach.