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A Credibility Model with Random Fluctuations in Delay Probabilities for the Prediction of IBNR Claims(*)

Published online by Cambridge University Press:  29 August 2014

Ole Hesselager  and
Thomas Witting
Ole Hesselager*
Affiliation:
University of Copenhagen, Denmark
Thomas Witting*
Affiliation:
Bavarian Reinsurance Company (Munich), FRG
*
Laboratory of Actuarial Math., University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark.
Bavarian Reinsurance Company, Sederanger 4–6, D-8000 Munich 22, BRD.
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Abstract

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We consider a general credibility model for the prediction of IBNR-claims which allows for random fluctuations in the underlying delay distribution. Such fluctuations always bring about decreasing credibility. It is shown that even negative credibility is achieved for more substantial fluctuations in the delay distribution. Special attention is paid to the mixed Poisson case for claim numbers including the discussion of parameter estimation.

Keywords

Credibility theoryIBNR-reservedelay distributionDirichlet distributionlinear sufficiency
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 18 , Issue 1 , April 1988 , pp. 79 - 90
Copyright
Copyright © International Actuarial Association 1988

Footnotes

(*)

Paper presented at the 1987 Oberwolfach Conference on Risk Theory, 20–26 September 1987.

References

Buhlmann, H., Schnieper, R. and Straub, E. (1980) Claims reserves in casualty insurance based on a probabilistic model. Bulletin of the Association of Swiss Actuaries 80/1, 21–45.Google Scholar
De Jong, P. and Zehnwirth, B. (1983) Claims reserving, state-space models and the Kalman filter. Journal of the Institute of Actuaries 110, 157–181.CrossRefGoogle Scholar
De Groot, M. H. (1970) Optimal Statistical Decisions. McGraw Hill, New York.Google Scholar
De Vylder, F. (1982) Estimation of IBNR claims by credibility theory. Insurance: Mathematics and Economics 1, 35–40.Google Scholar
Ferguson, T. S. (1973) A Bayesian analysis of some nonparametric problems. Annals of Statistics 1, 209–230.CrossRefGoogle Scholar
Hachemeister, C. A. (1975) Credibility for regression models with application to trends. In Credibility: Theory and Applications (ed. Kahn, P. M.), pp. 129–163. Academic Press, New York.Google Scholar
Jewell, W. S. (1976) Two classes of covariance matrices giving simple linear forecasts. Scandinavian Actuarial Journal 15–29.CrossRefGoogle Scholar
Norberg, R. (1986) A contribution to modelling of IBNR-claims. Scandinavian Actuarial Journal 155–203.CrossRefGoogle Scholar
Witting, T. (1987a) Kredibilitatsschatzungen fur die Anzahl IBNR-Schaden. “Blatter” of the German Association of Actuaries 18/1, 45–58.Google Scholar
Witting, T. (1987b) The linear Markov property in credibility theory. ASTIN Bulletin 17/1, 71–84.CrossRefGoogle Scholar
Zehnwirth, B. (1977) The mean credibility formula is a Bayes rule. Scandinavian Actuarial Journal 212–216.CrossRefGoogle Scholar