Montag, 09. Januar 2023, 16:45 - 17:45 iCal
ISOR Colloquium
"Bootstrap Consistency for the Mack Bootstrap"
Speaker: Carsten Jentsch (TU Dortmund University, Germany)
HS 7 OMP1 (#1.303)
Oskar-Morgenstern-Platz 1, 1090 Wien
Vortrag
Mack’s distribution-free chain ladder reserving model belongs to the most popular approaches in non-life insurance mathematics. While proposed to determine the first two moments of the reserve, it does not allow to identify the whole distribution of the reserve. For this purpose, Mack’s model is usually equipped with a tailor-made bootstrap procedure, which combines a residual-based non-parametric resampling step together with a parametric bootstrap. Although it is widely used in applications to estimate the reserve risk, no theoretical bootstrap consistency results exist that justify this approach.
In this paper, to fill this gap in the literature, we adopt the theoretical framework proposed by Steinmetz and Jentsch (2022, Insurance: Mathematics and Economics) to derive asymptotic theory in Mack’s model. By splitting the reserve into two additive parts corresponding to process and estimation uncertainty, it enables - for the first time - a rigorous investigation also of the validity of the Mack bootstrap. We prove that the (conditional) bootstrap distribution of the asymptotically dominating process uncertainty part is correctly mimicked if the parametric family of distributions of the individual development factors is correctly specified in Mack’s bootstrap proposal. Otherwise, this will be generally not the case. In contrast, the corresponding (conditional) bootstrap distribution of the estimation uncertainty part is generally not correctly captured. To tackle this, we propose an alternative Mack-type bootstrap, which is designed to capture also the distribution of the estimation uncertainty part.
We illustrate our findings in simulations and show that the newly proposed Mack-type bootstrap performs superior to the original Mack bootstrap in finite samples.
The talk also can be joined online via ZOOM: univienna.zoom.us/j/63751589259
Meeting room opens at: January 09, 2023, 4.30 pm Vienna
Meeting ID: 637 5158 9259
Password: 011511
Zur Webseite der Veranstaltung
Veranstalter
Institut für Statistik und Operations Research
Kontakt
Sabine Sobotka-Tompits, BA
Fakultät für Wirtschaftswissenschaften
Institut für Statistik und Operations Research
+43 1 4277 38631
sabine.sobotka-tompits@univie.ac.at
Erstellt am Montag, 28. November 2022, 11:51
Letzte Änderung am Montag, 28. November 2022, 13:48