Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-23T09:36:29.687Z Has data issue: false hasContentIssue false
  • English
  • Français

Prediction uncertainties in the Cape Cod reserving method

Published online by Cambridge University Press:  18 February 2015

Annina Saluz
Annina Saluz*
Affiliation:
Department of Mathematics, RiskLab, ETH Zurich, 8092 Zurich, Switzerland
*
*Correspondence to: Annina Saluz, Department of Mathematics, RiskLab, ETH Zurich, 8092 Zurich, Switzerland. Tel: +41 44 632 68 30; Fax: +41 44 632 15 23; E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The Cape Cod (CC) method was designed by Bühlmann and Straub in order to overcome some shortcomings of the chain ladder (CL) method. Owing to its simplicity and because of the advantages over the CL method, the CC method has become a well-established method in practice. In this paper we consider a distribution-free stochastic model for the CC method. Within this model we give the parameter estimates and we derive estimates for the conditional mean square error of prediction for the CC method. In addition, we derive an estimate for the uncertainty in the claims development result.

Keywords

Cape Cod methodClaims reservingMean square error of predictionClaims development result
Type
Papers
Information
Annals of Actuarial Science , Volume 9 , Issue 2 , September 2015 , pp. 239 - 263
Copyright
© Institute and Faculty of Actuaries 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alai, D.H., Merz, M. & Wüthrich, M.V. (2010). Prediction uncertainty in the Bornhuetter-Ferguson claims reserving method: revisited. Annals of Actuarial Science, 5(1), 7–17.Google Scholar
Bornhuetter, R.L. & Ferguson, R.E. (1972). Proceedings of the Casualty Actuarial Society. The actuary and IBNR. Proc. Cas, LIX, 181–195.Google Scholar
Bühlmann, H., De Felice, M., Gisler, A., Moriconi, F. & Wüthrich, M.V. (2009). Recursive credibility formula for chain ladder factors and the claims development result. ASTIN Bulletin, 39(1), 275–306.Google Scholar
Bühlmann, H. & Straub, E. (1983). Estimation of IBNR Reserves by the Methods Chain Ladder, Cape Cod and Complementary Loss Ratio. International Summer School of the Swiss Association of Actuaries, Leysin, Switzerland.Google Scholar
Dal Moro, E. & Lo, J. (2014). An industry question: the ultimate and one-year reserving uncertainty for different non-life reserving methodologies. ASTIN Bulletin, 44(3), 495–499.CrossRefGoogle Scholar
England, P.D. & Verrall, R.J. (2002). Stochastic claims reserving in general insurance. British Actuarial Journal, 8(3), 443–518.Google Scholar
FINMA (2006). Technisches Dokument zum Swiss Solvency Test, Version 02/10/2006, technical report, Bundesamt für Privatversicherungen, Bern, Switzerland.Google Scholar
Hachemeister, C. & Stanard, J. (1975). IBNR claims count estimation with static lag functions. ASTIN Colloquium, Portimao, Portugal. September 30 – October 3, 1975.Google Scholar
Mack, T. (1991). A simple parametric model for rating automobile insurance or estimating IBNR claims reserves. ASTIN Bulletin, 21(1), 93–109.Google Scholar
Mack, T. (1993). Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin, 23(2), 213–225.Google Scholar
Mack, T. (2006). Parameter estimation for Bornhuetter/Ferguson. CAS Forum, (Fall 2006), 141–157.Google Scholar
Mack, T. (2008). The prediction error of Bornhuetter/Ferguson. ASTIN Bulletin, 38(1), 87–103.CrossRefGoogle Scholar
Merz, M. & Wüthrich, M.V. (2008). Modelling the claims development result for solvency purposes. CAS Forum, (Fall 2008), 542–568.Google Scholar
Renshaw, A.E. & Verrall, R.J. (1998). A stochastic model for the chain ladder method. British Actuarial Journal, 14, 903–923.Google Scholar
Saluz, A., Gisler, A. & Wüthrich, M.V. (2011). Development pattern and prediction error for the stochastic Bornhuetter-Ferguson claims reserving method. ASTIN Bulletin, 41(2), 279–313.Google Scholar
Straub, E. (1988). Non-Life Insurance Mathematics. Springer-Verlag, Association of Swiss Actuaries, Zürich.Google Scholar
Taylor, G.C. (2002). Written discussion on the paper “Stochastic claims reserving in general insurance” by P. D. England and R. J. Verrall. British Actuarial Journal, 8(3), 540–542.Google Scholar
Wüthrich, M.V. & Merz, M. (2008). Stochastic Claims Reserving Methods in Insurance. Wiley, Chichester.Google Scholar