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Claim Reserving Using Distance-Based Generalized Linear Models

  • Eva BojEmail author
  • Teresa Costa
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 175)

Abstract

Generalized linear models (GLM) can be considered a stochastic version of the classical Chain-Ladder (CL) method of claim reserving in nonlife insurance. In particular, the deterministic CL model is reproduced when a GLM is fitted assuming over-dispersed Poisson error distribution and logarithmic link. Our aim is to propose the use of distance-based generalized linear models (DB-GLM) in the claim reserving problem. DB-GLM can be considered a generalization of the classical GLM to the distance-based analysis, because DB-GLM contains as a particular instance ordinary GLM when the Euclidean, \(l^2\), metric is applied. Then, DB-GLM can be considered too a stochastic version of the CL claim reserving method. In DB-GLM, the only information required is a predictor distance matrix. DB-GLM can be fitted using the dbstats package for R. To estimate reserve distributions and standard errors, we propose a nonparametric bootstrap technique adequate to the distance-based regression models. We illustrate the method with a well-known actuarial dataset.

Keywords

Reserving Chain-Ladder Generalized linear models Distance-based prediction dbstats. 

Notes

Acknowledgments

Work supported by the Spanish Ministerio de Educación y Ciencia, grant MTM2014-56535-R.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Facultat d’Economia i EmpresaUniversitat de BarcelonaBarcelonaSpain

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