Abstrakt
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 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 $\widehat{f}_j$. 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.