Asymptotic consistency and inconsistency of the chain ladder
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10125096" target="_blank" >RIV/00216208:11320/12:10125096 - isvavai.cz</a>
Result on the web
<a href="http://10.1016/j.insmatheco.2012.07.004" target="_blank" >http://10.1016/j.insmatheco.2012.07.004</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.insmatheco.2012.07.004" target="_blank" >10.1016/j.insmatheco.2012.07.004</a>
Alternative languages
Result language
angličtina
Original language name
Asymptotic consistency and inconsistency of the chain ladder
Original language description
The distribution-free chain ladder reserving method belongs to the most frequently used approaches in the general insurance. It is well known, see cite{Mack1993}, that the estimators $widehat{f}_{j}$ of the development factors are unbiased and mutuallyuncorrelated under some mild conditions on the mean structure and under the assumption of independence of the claims in different accident years. In this article we deal with some asymptotic properties of $widehat{f}_j$. Necessary and sufficient conditions for asymptotic consistency of the estimators of true development factors $f_j$ are provided. A~rate of convergence for the consistency is derived. Possible violation of these conditions and its consequences are discussed, and some practical recommendations are given. Numerical simulations and a~real data example are provided as well.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GBP402%2F12%2FG097" target="_blank" >GBP402/12/G097: DYME-Dynamic Models in Economics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Insurance: Mathematics and Economics
ISSN
0167-6687
e-ISSN
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Volume of the periodical
51
Issue of the periodical within the volume
2
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
8
Pages from-to
472-479
UT code for WoS article
000309028900027
EID of the result in the Scopus database
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