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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
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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