On Comparison of Stochastic Reserving Methods with Bootstrapping

Liivika Tee,Rauno Viin,Meelis Käärik

doi:10.3390/risks5010002

Abstract

We consider the well-known stochastic reserve estimation methods on the basis of generalized linear models, such as the (over-dispersed) Poisson model, the gamma model and the log-normal model. For the likely variability of the claims reserve, bootstrap method is considered. In the bootstrapping framework, we discuss the choice of residuals, namely the Pearson residuals, the deviance residuals and the Anscombe residuals. In addition, several possible residual adjustments are discussed and compared in a case study. We carry out a practical implementation and comparison of methods using real-life insurance data to estimate reserves and their prediction errors. We propose to consider proper scoring rules for model validation, and the assessments will be drawn from an extensive case study.

Highlights

Every non-life insurance company is obligated to compensate its policy holders for claims that meet the terms of the policy
We studied the impact of the methods and the residuals on the reserve estimates and their predictive distributions
We saw that the Poisson model and the gamma model tend to give similar point estimates, as expected, but there are bigger differences in the estimates of the prediction errors

Summary

Introduction

Every non-life insurance company is obligated to compensate its policy holders for claims that meet the terms of the policy. In order to meet and administer its contractual obligations to policyholders, the insurance company has to set up loss reserves. The focus has mainly been on aggregate reserving techniques, where models perform analysis with aggregate claims data. Considerable attention has been given to stochastic micro-level models, which use claims-related data on an individual basis, rather than aggregating by underwriting year and development period (for a reference, see [1,2,3]). Despite the fact that stochastic micro-level models have emerged in an increasing steam of academic literature, these models are not substantially used by practitioners

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