Robust Estimation of Reserve Risk

Marc Busse, Ulrich Müller and Michel Dacorogna

ASTIN Bulletin, 2010, vol. 40, issue 2, 453-489

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.

Date: 2010
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