Skip to main content Accessibility help
×
Home

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

  • Hans Bühlmann (a1), Massimo De Felice (a2), Alois Gisler (a3), Franco Moriconi (a4) and Mario V. Wüthrich (a5)...

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.

Copyright

References

Hide All
[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.
[2] Asmussen, S. and Glynn, P.W. (2007) Stochastic Simulation. Springer.
[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), 521542.
[4] Buhlmann, H. and Gisler, A. (2005) A Course in Credibility Theory and its Applications. Springer, Berlin.
[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.
[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.
[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.
[8] Gilks, W.R., Richardson, S. and Spiegelhalter, D.J. (1996) Markov Chain Monte Carlo in Practice. Chapman & Hall, London.
[9] Gisler, A. and Wüthrich, M.V. (2008) Credibility for the chain ladder reserving method. ASTIN Bulletin 38(2), 565600.
[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.
[11] Kremer, E. (1982) Credibility for some evolutionary models. Scand. Act. Journal 1982(3-4), 129142.
[12] Mack, T. (1993) Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin 23(2), 213225.
[13] Merz, M. and Wüthrich, M.V. (2008) Modelling the claims development result for solvency purposes. CAS E-Forum, Fall 2008, 542568.
[14] Ohlsson, E. and Lauzeningks, J. (2008) The one-year non-life insurance risk. Conference Paper, ASTIN Colloquium 2008, Manchester.
[15] Sundt, B. (1981) Recursive credibility estimation. Scand. Act. Journal 1981(1), 321.
[16] Wüthrich, M.V. and Merz, M. (2008) Stochastic Claims Reserving Methods in Insurance. Wiley.
[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.

Keywords

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

  • Hans Bühlmann (a1), Massimo De Felice (a2), Alois Gisler (a3), Franco Moriconi (a4) and Mario V. Wüthrich (a5)...

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