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Chain-Ladder as Maximum Likelihood Revisited

Published online by Cambridge University Press:  10 May 2011

D. Kuang ,
B. Nielsen  and
J. P. Nielsen
B. Nielsen
Affiliation:
Nuffield College, Oxford OX1 5AD, UK. :, Email: bent.nielsen@nuffield.ox.ac.uk
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Abstract

It has long been known that maximum likelihood estimation in a Poisson model reproduces the chain-ladder technique. We revisit this model. A new canonical parametrisation is proposed to circumvent the inherent identification problem in the parametrisation. The maximum likelihood estimators for the canonical parameter are simple, interpretable and easy to derive. The boundary problem where all observations in one particular development year or on particular underwriting year is zero is also analysed.

Keywords

Boundary ProblemCanonical ParameterChain-LadderIdentification ProblemMaximum LikelihoodPoisson Model
Type
Papers
Information
Annals of Actuarial Science , Volume 4 , Issue 1 , March 2009 , pp. 105 - 121
Copyright
Copyright © Institute and Faculty of Actuaries 2009

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