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A Method for Modelling Varying Run-Off Evolutions in Claims Reserving

Published online by Cambridge University Press:  29 August 2014

R.J. Verrall
R.J. Verrall*
Affiliation:
Department of Actuarial Science and Statistics, City University, London
*
Department of Actuarial Science and Statistics, City University, London.
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Abstract

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This paper considers the application of state space modelling to the chain ladder linear model in order to allow the run-off parameters to vary with accident year. In the usual application of the chain ladder technique, the development factors are assumed to be the same for each accident year. This implies that the run-off shape does not alter with accident year. This paper shows how this assumption can be relaxed in order to allow a recursive smooth model to be applied, or for large changes in the shape of the run-off curve. It is possible for these changes to be modelled using external inputs, or for a multiprocess model to be used to detect changes in the run-off shape.

Keywords

Chain ladder techniqueKalman filterlinear modelsstate space models
Type
Short Contributions
Information
ASTIN Bulletin: The Journal of the IAA , Volume 24 , Issue 2 , November 1994 , pp. 325 - 332
Copyright
Copyright © International Actuarial Association 1994

References

Kremer, E. (1982) IBNR-Claims and the Two-Way Model of ANOVA. Scand. Act. J., Vol. 1, 47–55.CrossRefGoogle Scholar
Renshwa, A.E. (1989) Chain Ladder and Interactive Modelling (Claims Reserving and Glim). Journal of the Institute of Actuaries 1989, Vol. 116, Part. III, 559–587.CrossRefGoogle Scholar
Taylor, G. C. and Ashe, F. R. (1983) Second Moments of Estimates of Outstanding Claims. J of Econometrics, Vol. 23, 37–61.CrossRefGoogle Scholar
Verrall, R.J. (1989) A State Space Representation of the Chain Ladder Linear Model. Journal of the Institute of Actuaries 1989, Vol. 116, Part. III, 589–610.CrossRefGoogle Scholar
Verrall, R.J. (1990) Bayes and Empirical Bayes Estimation for the Chain Ladder Model. ASTIN Bulletin 1990, Vol. 20, No. 2, 217–243.Google Scholar
Verrall, R.J. (1991a) On the Unbiased Estimation of Reserves from Loglinear Models. Insurance: Mathematics and Economics 1991, Vol. 10, No. 1, 75–80.Google Scholar
Verrall, R.J. (1991b) Chain Ladder and Maximum Likelihood. Journal of the Institute of Actuaries 1991, Vol. 118, Part. III, No. 471, 489–499.CrossRefGoogle Scholar