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A stochastic method for claims reserving in general insurance

Published online by Cambridge University Press:  20 April 2012

T. S. Wright
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Abstract

The paper addresses the problem of estimating future claim payments from the ‘run-off’ of past claim payments. A model of the claim payment process is postulated. Results from risk theory are applied to give a model for the incremental paid claims data by development period. A fitting method is developed which takes account of the error structure of the data implied by the underlying model of the claim payment process. The application of a similar method to incremental incurred data is considered. A numerical example is given.

Keywords

ClaimsGeneral InsuranceKalman filterReservesQuasi-likelihood
Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 117 , Issue 3 , December 1990 , pp. 677 - 731
Copyright
Copyright © Institute and Faculty of Actuaries 1990

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References

(1) Beard, R. E., Pentikainen, T. & Pesonen, E. (1969). Risk Theory—The Stochastic Basis of Insurance. (3rd Edition). Chapman & HallGoogle Scholar
(2) Craighead, D. H. (1979). Some Aspects of the London Reinsurance Market in World-Wide Short-Term Business. J.I.A. 106, 286.Google Scholar
(3) De Jong, P. & Zehnwirth, B. (1983). Claims Reserving, State-space Models and the Kalman Filter. J.I.A. 110, 157–182.Google Scholar
(4) Dobson, A. J. (1983). An Introduction to Statistical Modelling. Chapman & Hall.CrossRefGoogle Scholar
(5) Harrison, P. J. & Stephens, C. F. (1976). Bayesian Forecasting. Journal of the Royal Statistical Society (B) 38, 205.Google Scholar
(6) Hayne, R. (1989). Application of Collective Risk Theory to Estimate Variability in Loss Reserves. P.C.A.S.Google Scholar
(7) Jewell, W. S. (1989). Predicting IBNYR Events and Delays. ASTIN Bulletin, 19, 25–56.CrossRefGoogle Scholar
(8) Kremer, E. (1982). IBNR-Claims and the Two-Way Model of ANOVA. Scand. Act. J. 1, 47–55.CrossRefGoogle Scholar
(9) McCullagh, P. & Nelder, J. A. (1983). Generalised Linear Models. Chapman & Hall.CrossRefGoogle Scholar
(10) Renshaw, A. E. (1989). Chain Ladder and Interactive Modelling (Claims Reserving and GLIM). J.I.A. 116, 559–587.Google Scholar
(11) Sherman, R. E. (1984). Extrapolating, Smoothing and Interpolating Development Factors. P.C.A.S. LXXI, 122–192.Google Scholar
(12) Verrall, R. J. (1989). A State Space Representation of the Chain Ladder Linear Model. J.I.A. 116, 589–609.Google Scholar
(13) Zehnwirth, B. (1985). ICRFS Version 4 Manual and Users Guide. Benhar Nominees Pty Ltd, Turramurra, N.S.W., Australia.Google Scholar