Asymptotic Consistency and Inconsistency of the Chain Ladder

• Activity Number: 488
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Risk Analysis
• Author(s): Michal Pesta*+ and Sarka Hudecova
• Companies: Charles University in Prague and Charles University in Prague
• Keywords: property and casualty insurance ; actuarial science ; stochastic reserving ; claims reserving ; chain ladder ; asymptotic properties

Abstract

The distribution-free chain ladder reserving method belongs to the most frequently used approaches in the general insurance. It is well known, see [1], 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 [2], 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.

References:

[1] Mack, T. (1993). Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin, 23, 2, 213-225.

[2] Pesta, M. and Hudecova, S. (2012). Asymptotic consistency and inconsistency of the chain ladder. Insurance: Mathematics and Economics, 51, 2, 472-479.