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A generalized linear model with smoothing effects for claims reserving

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  • Björkwall, Susanna
  • Hössjer, Ola
  • Ohlsson, Esbjörn
  • Verrall, Richard

Abstract

In this paper, we continue the development of the ideas introduced in England and Verrall (2001) by suggesting the use of a reparameterized version of the generalized linear model (GLM) which is frequently used in stochastic claims reserving. This model enables us to smooth the origin, development and calendar year parameters in a similar way as is often done in practice, but still keep the GLM structure. Specifically, we use this model structure in order to obtain reserve estimates and to systemize the model selection procedure that arises in the smoothing process. Moreover, we provide a bootstrap procedure to achieve a full predictive distribution.

Suggested Citation

  • Björkwall, Susanna & Hössjer, Ola & Ohlsson, Esbjörn & Verrall, Richard, 2011. "A generalized linear model with smoothing effects for claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 27-37, July.
    • Handle: RePEc:eee:insuma:v:49:y:2011:i:1:p:27-37
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    References listed on IDEAS

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    1. Katrien Antonio & Jan Beirlant, 2008. "Issues in Claims Reserving and Credibility: A Semiparametric Approach With Mixed Models," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(3), pages 643-676, September.
    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. Renshaw, A.E. & Verrall, R.J., 1998. "A Stochastic Model Underlying the Chain-Ladder Technique," British Actuarial Journal, Cambridge University Press, vol. 4(4), pages 903-923, October.
    4. Verrall, R.J. & England, P.D., 2005. "Incorporating expert opinion into a stochastic model for the chain-ladder technique," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 355-370, October.
    5. Verrall, Richard, 1996. "Claims reserving and generalised additive models," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 31-43, December.
    6. Taylor, G. C. & Ashe, F. R., 1983. "Second moments of estimates of outstanding claims," Journal of Econometrics, Elsevier, vol. 23(1), pages 37-61, September.
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    Cited by:

    1. Hudecová, Šárka & Pešta, Michal, 2013. "Modeling dependencies in claims reserving with GEE," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 786-794.
    2. Stefano Cavastracci Strascia & Agostino Tripodi, 2018. "Overdispersed-Poisson Model in Claims Reserving: Closed Tool for One-Year Volatility in GLM Framework," Risks, MDPI, vol. 6(4), pages 1-24, December.

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