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The Prediction Error of Bornhuetter/Ferguson

Published online by Cambridge University Press:  17 April 2015

Thomas Mack
Thomas Mack*
Affiliation:
Munich, Germany, E-Mail: tmack@gmx.net
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Abstract

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Together with the Chain Ladder (CL) method, the Bornhuetter/Ferguson (BF) method is one of the most popular claims reserving methods. Whereas a formula for the prediction error of the CL method has been published already in 1993, there is still nothing equivalent available for the BF method. On the basis of the BF reserve formula, this paper develops a stochastic model for the BF method. From this model, a formula for the prediction error of the BF reserve estimate is derived.

Moreover, the model gives important advice on how to estimate the parameters for the BF reserve formula. E.g. it turns out that the appropriate BF development pattern is different from the CL pattern. This is a nice add-on as it makes BF to a standalone reserving method which is fully independent from CL. The other parameter required for the BF reserve is the well-known initial estimate for the ultimate claims amount. Here the stochastic model clearly shows what has to be meant with ‘initial’.

In order to apply the formula for the prediction error, the actuary must assess his uncertainty about both sets of parameters, about the development pattern and about the initial ultimate claims estimates. But for both, much guidance can be drawn from the estimates itself and from the run-off data given. Finally, a numerical example shows how the resulting prediction error compares to the one of the CL method.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 38 , Issue 1 , May 2008 , pp. 87 - 103
Copyright
Copyright © ASTIN Bulletin 2008

References

Bornhuetter, R.L. and Ferguson, R.E. (1972) The Actuary and IBNR. Proceedings of the CAS, LIX, 181–195.Google Scholar
Mack, Th. (1993) Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates. ASTIN Bulletin, 23, 213–225.CrossRefGoogle Scholar
Mack, Th. (1999) The Standard Error of Chain Ladder Reserve Estimates: Recursive Calculation and Inclusion of a Tail Factor. ASTIN Bulletin, 29, 361–366.CrossRefGoogle Scholar
Mack, Th. (2006) Parameter Estimation for Bornhuetter/Ferguson. CAS Forum Fall 2006, 141–157.Google Scholar
Taylor, G.C. (2002) Written discussion of the paper “Stochastic Claims Reserving in General Insurance” by England, P.D. and Verrall, R.J.,British Actuarial Journal, 8, Part III (2002), 540–542.Google Scholar