Claims reserving and generalised additive models. (English) Zbl 0894.62114

Summary: This paper shows how nonparametric smoothing can be applied in the context of claims reserving. The paper concentrates on the chain-ladder technique, within the framework of the chain-ladder linear model, but the methods can easily be applied to other models. It is shown that non-parametric smoothing can provide more stable reserve estimates, and is an alternative to other methods suggested for this purpose such as the Kalman filter. The methods are implemented in the statistical package S-PLUS.


62P05 Applications of statistics to actuarial sciences and financial mathematics
62G07 Density estimation
65C99 Probabilistic methods, stochastic differential equations


Full Text: DOI


[1] Chambers, J.M.; Hastie, T.J., Statistical models in S, (1992), Chapman and Hall London · Zbl 0776.62007
[2] De Jong, P.; Zehnwirth, B., Claims reserving, state-space models and the Kalman filter, Jia, 110, 157, (1983)
[3] Gavin, J.B.; Haberman, S.; Verrall, R.J., Moving weighted average graduation using kernel graduation, Insurance: mathematics and economics, 12, 113-126, (1993) · Zbl 0778.62096
[4] Gavin, J.B.; Haberman, S.; Verrall, R.J., On the choice of bandwidth for kernel graduation, Jia, 121, 119-134, (1994)
[5] Gavin, J.B.; Haberman, S.; Verrall, R.J., Variable kernel graduation with a boundary correction, Transactions of society of actuaries, (1995), to appear
[6] Hastie, T.; Tibshirani, R., Generalized additive models, (1990), Chapman and Hall London · Zbl 0747.62061
[7] Hastie, T.; Tibshirani, R., Varying coefficient models (with discussion), JRSS, series B, 55, 757-796, (1993) · Zbl 0796.62060
[8] Kyriokidou, M., Claims reserving using generalized additive models in S-PLUS, ()
[9] Mack, T., Which stochastic model is underlying the chain ladder method?, () · Zbl 0818.62093
[10] Nelder, J.; Pregibon, D., An extended quasi-likelihood function, Biometrika, 74, 221-231, (1987) · Zbl 0621.62078
[11] Renshaw, A.E., Chain ladder and interactive modelling (claims reserving and GLIM), Jia, 116, 559-587, (1989)
[12] Renshaw, A.E., On the second moment properties and the implementation of certain GLIM based stochastic claims reserving models, ()
[13] Renshaw, A.E.; Verrall, R.J., A stochastic model underlying the chain-ladder technique, ()
[14] Silverman, B.W., Density estimation for statistics and data analysis, (1986), Chapman and Hall London · Zbl 0617.62042
[15] Venables, W.N.; Ripley, B.D., Modern applied statistics with S-PLUS, (1994), Springer Berlin · Zbl 0806.62002
[16] Verrall, R.J., A state space representation of the chain ladder linear model, Jia, 116, 589-610, (1989)
[17] Verrall, R.J., Bayes and empirical Bayes estimation for the chain ladder model, ASTIN bulletin, 20, 217-243, (1990)
[18] Verrall, R.J., On the estimation of reserves from loglinear models, Insurance: mathematics and economics, 10, 75-80, (1991) · Zbl 0723.62070
[19] Wedderburn, R.W.M., Quasi-likelihood functions, generalized linear models and the Gauss-Newton method, Biometrika, 61, 439-447, (1974) · Zbl 0292.62050
[20] West, M.; Harrison, J.; Migon, H., Dynamic generalised linear models and Bayesian forecasting (with discussion), Journal of the American statistical association, 80, 73-97, (1985) · Zbl 0568.62032
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.