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Recursive Credibility Formula for Chain Ladder Factors and the Claims Development Result

Published online by Cambridge University Press:  09 August 2013

Hans Bühlmann ,
Massimo De Felice ,
Alois Gisler ,
Franco Moriconi  and
Mario V. Wüthrich
Hans Bühlmann
Affiliation:
Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland, E-mail: hbuhl@math.ethz.ch
Massimo De Felice
Affiliation:
Dipartimento di Studi Sociali, Economici, Aattuariali e Finanziari, Viale Regina Elena, 295, 00161 Roma, Italy, E-mail: massimo.defelice@uniroma1.it
Alois Gisler
Affiliation:
AXA Winterthur Insurance Company, P.O. Box 357, 8401 Winterthur, Switzerland, E-mail: alois.gisler@axa-winterthur.ch
Franco Moriconi
Affiliation:
Dipartimento di Economia, Finanza e Statistica, Università di Perugia, Via A. Pascoli, 1, 06100 Perugia, Italy, E-mail: moriconi@unipg.it
Mario V. Wüthrich
Affiliation:
Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland, E-mail: wueth@math.ethz.ch
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Abstract

In recent Solvency II considerations much effort has been put into the development of appropriate models for the study of the one-year loss reserving uncertainty in non-life insurance. In this article we derive formulas for the conditional mean square error of prediction of the one-year claims development result in the context of the Bayes chain ladder model studied in Gisler-Wüthrich. The key to these formulas is a recursive representation for the results obtained in Gisler-Wüthrich.

Keywords

Claims reservingchain ladder methodcredibility chain ladder methodclaims development resultyear end expectationloss experience prior accident yearsliability at maturitysolvencymean square error of prediction

Information

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 39 , Issue 1 , May 2009 , pp. 275 - 306
Copyright
Copyright © International Actuarial Association 2009

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References

[1] AISAM-ACME (2007) AISAM-ACME study on non-life long tail liabilities. Reserve risk and risk margin assessment under Solvency II. October 17, 2007.Google Scholar
[2] Asmussen, S. and Glynn, P.W. (2007) Stochastic Simulation. Springer.Google Scholar
[3] Buchwalder, M., Bühlmann, H., Merz, M. and Wüthrich, M.V. (2006) The mean square error of prediction in the chain ladder reserving method (Mack and Murphy revisited). ASTIN Bulletin 36(2), 521–542.CrossRefGoogle Scholar
[4] Buhlmann, H. and Gisler, A. (2005) A Course in Credibility Theory and its Applications. Springer, Berlin.Google Scholar
[5] De Felice, M. and Moriconi, F. (2003) Risk based capital in P&C loss reserving or stressing the triangle. Research Group on “Insurance Companies and Pension Funds”, Working Paper n. 1, Rome, December 2003.Google Scholar
[6] De Felice, M. and Moriconi, F. (2006) Process error and estimation error of year-end reserve estimation in the distribution free chain-ladder model. Alef Working Paper, Rome, November 2006.Google Scholar
[7] Gerber, H.U. and Jones, D.A. (1975) Credibility formulas of the updating type. In Kahn, P.M. (ed.), Credibility: Theory and Applications. Academic Press.Google Scholar
[8] Gilks, W.R., Richardson, S. and Spiegelhalter, D.J. (1996) Markov Chain Monte Carlo in Practice. Chapman & Hall, London.Google Scholar
[9] Gisler, A. and Wüthrich, M.V. (2008) Credibility for the chain ladder reserving method. ASTIN Bulletin 38(2), 565–600.CrossRefGoogle Scholar
[10] ISVAP (2006) Reserve requirements and capital requirements in non-life insurance. An analysis of the Italian MTPL insurance market by stochastic claims reserving models. Report prepared by De Felice, M., Moriconi, F., Matarazzo, L., Cavastracci, S. and Pasqualini, S., Rome, October 2006.Google Scholar
[11] Kremer, E. (1982) Credibility for some evolutionary models. Scand. Act. Journal 1982(3-4), 129–142.Google Scholar
[12] Mack, T. (1993) Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin 23(2), 213–225.Google Scholar
[13] Merz, M. and Wüthrich, M.V. (2008) Modelling the claims development result for solvency purposes. CAS E-Forum, Fall 2008, 542–568.Google Scholar
[14] Ohlsson, E. and Lauzeningks, J. (2008) The one-year non-life insurance risk. Conference Paper, ASTIN Colloquium 2008, Manchester.Google Scholar
[15] Sundt, B. (1981) Recursive credibility estimation. Scand. Act. Journal 1981(1), 3–21.CrossRefGoogle Scholar
[16] Wüthrich, M.V. and Merz, M. (2008) Stochastic Claims Reserving Methods in Insurance. Wiley.Google Scholar
[17] Wüthrich, M.V., Merz, M. and Lysenko, N. (2008) Uncertainty in the claims development result in the chain ladder method. Accepted for publication in Scand. Act. J. Google Scholar