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Dispersion modelling of outstanding claims with double Poisson regression models

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  • Gao, Guangyuan
  • Meng, Shengwang
  • Shi, Yanlin

Abstract

Over-dispersed Poisson chain-ladder models are widely used in general insurance claims reserving. Although such models can accommodate the over-dispersion frequently observed in run-off triangles, they also impose an additional constraint of fixed variance to mean ratio across cells. In this paper, we relax this constraint and develop a flexible dispersion structure in a double Poisson chain-ladder model. The proposed model nests the classic over-dispersed Poisson model as a special case. A generalized likelihood ratio test is further proposed to compare different dispersion structures. In contrast to the existing claims reserving methods, our proposed method is more flexible in terms of the dispersion modelling. Simulation and empirical studies are conducted to demonstrate the importance of flexible dispersion modelling.

Suggested Citation

  • Gao, Guangyuan & Meng, Shengwang & Shi, Yanlin, 2021. "Dispersion modelling of outstanding claims with double Poisson regression models," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 572-586.
    • Handle: RePEc:eee:insuma:v:101:y:2021:i:pb:p:572-586
    DOI: 10.1016/j.insmatheco.2021.10.002
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    References listed on IDEAS

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    More about this item

    Keywords

    Incurred but not reported (IBNR) claims; Double Poisson distribution; Approximate restricted or residual maximum likelihood (approximate REML); Chain-ladder technique; Over-dispersed Poisson model; Prediction error;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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