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Stochastic Claims Reserving in Insurance Using Random Effects

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  • Michal Gerthofer
  • Michal Pešta

Abstract

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.

Suggested Citation

  • Michal Gerthofer & Michal Pešta, 2017. "Stochastic Claims Reserving in Insurance Using Random Effects," Prague Economic Papers, Prague University of Economics and Business, vol. 2017(5), pages 542-560.
    • Handle: RePEc:prg:jnlpep:v:2017:y:2017:i:5:id:625:p:542-560
    DOI: 10.18267/j.pep.625
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    References listed on IDEAS

    as
    1. Antonio, Katrien & Beirlant, Jan, 2007. "Actuarial statistics with generalized linear mixed models," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 58-76, January.
    2. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(3), pages 443-518, August.
    3. Pešta, Michal & Okhrin, Ostap, 2014. "Conditional least squares and copulae in claims reserving for a single line of business," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 28-37.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Martin Hrba & Matúš Maciak & Barbora Peštová & Michal Pešta, 2022. "Bootstrapping Not Independent and Not Identically Distributed Data," Mathematics, MDPI, vol. 10(24), pages 1-26, December.
    2. Maciak, Matúš & Okhrin, Ostap & Pešta, Michal, 2021. "Infinitely stochastic micro reserving," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 30-58.

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    More about this item

    Keywords

    claims reserving; non-life insurance; dependency modelling; random effects; mixed models; GLM; GLMM; panel data;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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