Skip to main content Accessibility help
×
Home

CHAIN LADDER AND ERROR PROPAGATION

  • Ancus Röhr (a1)

Abstract

We show how estimators for the chain ladder prediction error in Mack's (1993) distribution-free stochastic model can be derived using the error propagation formula. Our method allows for the treatment of the general case of the prediction error of the loss development result between two arbitrary future horizons. In the well-known special cases considered previously by Mack (1993) and Merz and Wüthrich (2008), our estimators coincide with theirs. However, the algebraic form in which we cast them is new, considerably more compact and more intuitive to understand. For example, in the classical case treated by Mack (1993), we show that the mean squared prediction error divided by the squared estimated ultimate loss can be written as jû2j, where ûj measures the (relative) uncertainty around the jth development factor and the proportion of the estimated ultimate loss that it affects. The error propagation method also provides a natural split into process error and parameter error. Our proofs identify and exploit symmetries of “chain ladder processes” in a novel way. For the sake of wider practical applicability of the formulae derived, we allow for incomplete historical data and the exclusion of outliers in the triangles.

Copyright

References

Hide All
Buchwalder, M., Bühlmann, H., Merz, M. and Wüthrich, M. (2006) The mean square error of prediction in the chain ladder reserving method (Mack and Murphy Revisited), ASTIN Bulletin, 36 (2), 521542.
Bühlmann, H., De Felice, M., Gisler, A., Moriconi, F. and Wüthrich, M.V. (2009) Recursive credibility formula for chain ladder factors and the claims development result. ASTIN Bulletin, 39 (1), 275306.
Dahms, R. (2008) A loss reserving method for incomplete data. Mitteilungen-Bulletin SAV, 1–2, 127148.
Gisler, A. (2013) “Die rasante Entwicklung der Mathematik in der Versicherung: eine Zeitreise über die letzten 30 Jahre”. Presentation given at the annual conference of the Swiss Actuarial Association in Winterthur, 7 September 2013.
Ku, H.H. (1966) Notes on the use of propagation of error formulas. Journal of Research of the National Bureau of Standards - C. Engineering and Instrumentation, 70C (4), 263273.
Mack, T. (1993) Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin, 23 (2), 213225.
Mack, T. (2008) The prediction error of Bornhuetter/Ferguson. ASTIN Bulletin, 38 (1), 87103.
Matitschka, H. (2010) Prognosefehler im Overdispersed Poisson Modell für Abwicklungsdreiecke. Blätter DGVFM, 31, 291306.
Merz, M. and Wüthrich, M.V. (2008). Modelling the claims development result for solvency purposes. CAS E-Forum Fall 2008, 542–568.
Merz, M. and Wüthrich, M.V. (2014) Claims run-off uncertainty: The full picture, http://ssrn.com/abstract=2524352
Salzmann, R. and Wüthrich, M.V. (2010) Cost-of-capital margin for a general insurance liability runoff, ASTIN Bulletin, 40/2, 415451.
Taylor, G.C. and Ashe, F.R. (1983) Second moments of estimates of outstanding claims. Journal of Econometrics, 23, 3761.
Wüthrich, M.V. and Merz, M. (2008) Stochastic Claims Reserving Methods in Non-Life Insurance. New York: Wiley.

Keywords

CHAIN LADDER AND ERROR PROPAGATION

  • Ancus Röhr (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed