Asymptotic consistency and inconsistency of the chain ladder

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Asymptotic consistency and inconsistency of the chain ladder

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Asymptotic consistency and inconsistency of the chain ladder

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GBP402%2F12%2FG097" target="_blank" >GBP402/12/G097: DYME-Dynamické modely v ekonomii</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2012

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Insurance: Mathematics and Economics

ISSN

0167-6687

e-ISSN

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Svazek periodika

51

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

8

Strana od-do

472-479

Kód UT WoS článku

000309028900027

EID výsledku v databázi Scopus

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