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Predictive Distributions for Reserves which Separate True IBNR and IBNER Claims

  • Huijuan Liu and Richard Verrall (a1)

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.

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References

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Bornhuetter, R.L. and Ferguson, R.E. (1972) The Actuary and IBNR Proc. CAS. Act. Soc., LIX, 181195.
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), 522542.
Gisler, A. (2006) The Estimation Error in the Chain ladder Reserving Method: A Bayesian Approach. ASTIN Bulletin, 36(2), 555571.
Gisler, A. and Wuthrich, M.V. (2008) Credibility for the chain ladder reserving method. ASTIN Bulletin, 38(2), 565600.
England, P.D. and Verrall, R.J. (2002) Stochastic Claims Reserving in General Insurance (with discussion). British Actuarial Journal, 8, 443544.
Mack, T. (1993) Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin 23(2), 214225.
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), 544552.
Schnieper, R. (1991) Separating True IBNR and IBNER Claims. ASTIN Bulletin 21(1), 111127.
Taylor, G.C. (2000) Loss Reserving: An Actuarial Perspective, Kluwer.
Verrall, R.J. (2000) An Investigation into Stochastic Claims Reserving Models and the Chain ladder Technique. Insurance: Mathematics and Economics, 26, 9199.
Verrall, R.J. (2004) A Bayesian Generalised Linear Model for the Bornhuetter-Ferguson Method of Claims Reserving. North American Actuarial Journal, 8(3), 6789.
Venter, G.G. (2006) Discussion of Mean Square Error of Prediction in the Chain Ladder Reserving Method. ASTIN Bulletin, 36(2), 568571.
Wuthrich, M.V. and Merz, M. (2008) Stochastic Claims Reserving Methods in Insurance. Wiley.

Keywords

Predictive Distributions for Reserves which Separate True IBNR and IBNER Claims

  • Huijuan Liu and Richard Verrall (a1)

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