Prague Economic Papers 2017, 26(5):542-560 | DOI: 10.18267/j.pep.625

Stochastic Claims Reserving in Insurance Using Random Effects

Michal Gerthofer1, Michal Pešta2
1 Faculty of Informatics and Statistics, Department of Statistics and Probability, University of Economics in Prague, Prague, Czech Republic (Michal.Gerthofer@gmail.com)
2 Faculty of Mathematics and Physics, Department of Probability and Mathematical Statistics, Charles University in Prague, Prague, Czech Republic (Michal.Pesta@mff.cuni.cz)

Estimation of claims reserves, which should be held by the insurer so as to be able to meet expected future claims arising from policies currently in force and policies written in the past, presents an important task for insurance companies to predict their liabilities. A common approach to the reser-ving problem is based on generalized linear models (GLM). In this article, the application of genera-lized linear mixed models (GLMM) - an extension of the GLM - for estimation of the loss reserves is shown. Since the GLMM allows incorporating a random effect instead of several fixed effects corresponding to the accident years as in case of the GLM, volatility of the prediction is reduced. This allows more flexible risk valuation, which is a crucial element of risk management and capital allocation practices of non-life insurers. A real data example together with diagnostics for the model selection are provided as an illustration of the potential benefits of the presented approach.

Keywords: claims reserving, non-life insurance, dependency modelling, random effects, mixed models, GLM, GLMM, panel data
JEL classification: C13, C18, C23, C33, C51, G22

Published: October 1, 2017  Show citation

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Gerthofer, M., & Pešta, M. (2017). Stochastic Claims Reserving in Insurance Using Random Effects. Prague Economic Papers, 26(5), 542-560. doi: 10.18267/j.pep.625
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