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Predictive Distributions for Reserves which Separate True IBNR and IBNER Claims

Published online by Cambridge University Press:  09 August 2013

Huijuan Liu  and
Richard Verrall
Richard Verrall
Affiliation:
Faculty of Actuarial Science and Insurance, Cass Business School, City University, 106 Bunhill Row, London EC1Y 8TZ, E-Mail: [email protected], Tel: 0207 040 8476
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Abstract

This paper considers the model suggested by Schnieper (1991), which separates the true IBNR claims from the IBNER. Stochastic models are defined, using both recursive and non-recursive procedures, within the framework of the models described in England and Verrall (2002). Approximations to the prediction error of the reserves are derived analytically.

Some extensions to the original Schnieper model are also disussed, together with other possible applications of this type of model.

Keywords

Bornhuetter-Fergusonchain ladderclaims reservingpredictive distribution
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 39 , Issue 1 , May 2009 , pp. 35 - 60
Copyright
Copyright © International Actuarial Association 2009

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References

Bornhuetter, R.L. and Ferguson, R.E. (1972) The Actuary and IBNR Proc. CAS. Act. Soc., LIX, 181–195.Google Scholar
Buchwalder, M., Buhlmann, H., Merz, M. and Wuthrich, M.V. (2006) The Mean Square Error of Prediction in the Chain Ladder Reserving Method (Mack and Murphy revisited). ASTIN Bulletin, 36(2), 522–542.Google Scholar
Gisler, A. (2006) The Estimation Error in the Chain ladder Reserving Method: A Bayesian Approach. ASTIN Bulletin, 36(2), 555–571.CrossRefGoogle Scholar
Gisler, A. and Wuthrich, M.V. (2008) Credibility for the chain ladder reserving method. ASTIN Bulletin, 38(2), 565–600.Google Scholar
England, P.D. and Verrall, R.J. (2002) Stochastic Claims Reserving in General Insurance (with discussion). British Actuarial Journal, 8, 443–544.Google Scholar
Mack, T. (1993) Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin 23(2), 214–225.Google Scholar
Mack, T., Quarg, G. and Braun, C. (2006) The Mean Square Error of Prediction in the Chain Ladder Reserving Method – A Comment. ASTIN Bulletin, 36(2), 544–552.Google Scholar
Schnieper, R. (1991) Separating True IBNR and IBNER Claims. ASTIN Bulletin 21(1), 111–127.Google Scholar
Taylor, G.C. (2000) Loss Reserving: An Actuarial Perspective, Kluwer.Google Scholar
Verrall, R.J. (2000) An Investigation into Stochastic Claims Reserving Models and the Chain ladder Technique. Insurance: Mathematics and Economics, 26, 91–99.Google Scholar
Verrall, R.J. (2004) A Bayesian Generalised Linear Model for the Bornhuetter-Ferguson Method of Claims Reserving. North American Actuarial Journal, 8(3), 67–89.Google Scholar
Venter, G.G. (2006) Discussion of Mean Square Error of Prediction in the Chain Ladder Reserving Method. ASTIN Bulletin, 36(2), 568–571.CrossRefGoogle Scholar
Wuthrich, M.V. and Merz, M. (2008) Stochastic Claims Reserving Methods in Insurance. Wiley.Google Scholar