Montag, 03. Dezember 2018, 16:45 - 17:45 iCal
ISOR Colloquium
"Robust risk aggregation with neural networks (joint work with Stephan Eckstein and Michael Kupper)"
Speaker: Mathias Pohl (ISOR)
HS 7 (#1.303), 1st floor
Oskar-Morgenstern-Platz 1, 1090 Wien
Vortrag
We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of dependence structure, and that the marginal distributions are known. Furthermore, a current best guess for a distribution, called reference measure, is available. We work with the set of distributions that are both close to the given reference measure in a transportation distance (e.g. the Wasserstein distance), and additionally have the correct marginal structure. The goal is to find upper and lower bounds for integrals of interest with respect to distributions in this set. The described problem appears naturally in the context of risk aggregation. When aggregating different risks, the marginal distributions of these risks are known and the task is to quantify their joint effect on a given system. This is typically done by applying a meaningful risk measure to the sum of the individual risks. For this purpose, the stochastic interdependencies between the risks need to be specified. In practice the models of this dependence structure are however subject to relatively high model ambiguity. The contribution of this paper is twofold: Firstly, we derive a dual representation of the considered problem and prove that strong duality holds. Secondly, we propose a generally applicable and computationally feasible method, which relies on neural networks, in order to numerically solve the derived dual problem. The latter method is tested on a number of toy examples, before it is finally applied to perform robust risk aggregation in a real world instance.
Zur Webseite der Veranstaltung
Veranstalter
Institut für Statistik und Operations Research
Kontakt
Mag. Vera Lehmwald
Fakultät für Wirtschaftswissenschaften
Institut für Statistik und Operations Research
+43 1 4277 38651
vera.lehmwald@univie.ac.at
Erstellt am Dienstag, 27. November 2018, 13:16
Letzte Änderung am Montag, 10. Dezember 2018, 09:41