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Asymptotic consistency and inconsistency of the chain ladder

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  • Pešta, Michal
  • Hudecová, Šárka
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    Abstract

    The distribution-free chain ladder reserving method belongs to the most frequently used approaches in general insurance. It is well known, see Mack (1993), that the estimators f̂j of the development factors are unbiased and mutually uncorrelated 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 f̂j. Necessary and sufficient conditions for asymptotic consistency of the estimators of true development factors fj 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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167668712000832
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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 51 (2012)
    Issue (Month): 2 ()
    Pages: 472-479

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    Handle: RePEc:eee:insuma:v:51:y:2012:i:2:p:472-479

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: IM10; IM20; Claims reserving; Chain ladder; Asymptotic properties; Development factors;

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    References

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    1. Taylor, G. C. & Ashe, F. R., 1983. "Second moments of estimates of outstanding claims," Journal of Econometrics, Elsevier, vol. 23(1), pages 37-61, September.
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    Cited by:
    1. Hudecová, Šárka & Pešta, Michal, 2013. "Modeling dependencies in claims reserving with GEE," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 786-794.
    2. Pešta, Michal & Okhrin, Ostap, 2014. "Conditional least squares and copulae in claims reserving for a single line of business," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 28-37.

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