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EXISTENCE AND UNIQUENESS OF CHAIN LADDER SOLUTIONS

Published online by Cambridge University Press:  12 August 2016

Greg Taylor
Greg Taylor*
Affiliation:
UNSW Business School, Level 6, West Lobby, UNSW Business School Building E12, UNSW Sydney 2052Australia E-Mail: gregory.taylor@unsw.edu.au
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Abstract

The cross-classified chain ladder has a number of versions, depending on the distribution to which observations are subject. The simplest case is that of Poisson distributed observations, and then maximum likelihood estimates of parameters are explicit. Most other cases, however, including Bayesian chain ladder models, lead to implicit MAP (Bayesian) or MLE (non-Bayesian) solutions for these parameter estimates, raising questions as to their existence and uniqueness. The present paper investigates these questions in the case where observations are distributed according to some member of the exponential dispersion family.

Keywords

Bayesian chain laddercross-classified chain ladderEDF chain ladderexistenceloss reservingMAP estimatormaximum likelihood estimateTweedie chain ladderuniqueness
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 47 , Issue 1 , January 2017 , pp. 1 - 41
Copyright
Copyright © Astin Bulletin 2016 

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