Abstract
We tackle problems that appear in the practical application of the Mack method for the estimation of reserving risk and the bootstrapping of ultimate reserve distributions. More specifically, we design a filter for outliers and large jumps, and present a robust version of Mack’s variance estimator. A combination of these guarantees a reasonable Mack and bootstrap error even for deficient data. Furthermore, a method is derived that allows us to remove the influence of fluctuations in earning patterns from the reserve risk estimate. It is thereby shown that the relation between underwriting and accident year based loss development patterns is given by a convolution. A numerically stable inversion thereof is obtained by means of a Tikhonov regularization. The reliability of the presented methods is verified with several loss triangles.
Keywords: Reserve risk, stochastic reserves, dynamic financial analysis, Mack method, bootstrap, robust statistics, Tikhonov regularization, inverse problems.
Volume
Vol. 40, No. 2
Page
1-37
Year
2010
Categories
Financial and Statistical Methods
Statistical Models and Methods
Boot-Strapping and Resampling Methods
Actuarial Applications and Methodologies
Data Management and Information
Data Collection and Statistical Reporting
Actuarial Applications and Methodologies
Dynamic Risk Modeling
Dynamic Financial Analysis (DFA);
Actuarial Applications and Methodologies
Reserving
Publications
ASTIN Bulletin
