Seminar by Dr. Marius HOFERT from University of Waterloo

A novel approach based on generative neural networks is introduced for constructing quasi-random number generators for multivariate distributions specified by a copula in order to estimate expectations with variance reduction. So far, quasi-random number generators for multivariate distributions required a careful design, exploiting specific properties (such as conditional distributions) of the implied copula or the underlying quasi-Monte Carlo point set, and were only tractable for a small number of models. Utilizing specific generative neural networks allows one to construct quasi-random number generators for a much larger variety of multivariate distributions without such restrictions. Once trained with a pseudo-random sample, these neural networks only require a multivariate standard uniform randomized quasi-Monte Carlo point set as input and are thus fast in estimating expectations under dependence with variance reduction. Numerical examples are considered to demonstrate the approach. Emphasis is put on ideas rather than mathematical proofs.

Dr. Marius Hofert is an Associate Professor in the Department of Statistics and Actuarial Science at University of Waterloo. He completed a diploma in Mathematics and Management at University of Ulm, a masters degree in Mathematics at Syracuse University and obtained his PhD in Mathematics from University of Ulm in 2010. He then held a postdoctoral research position (Willis Research Fellow) at RiskLab, ETH Zurich, under the supervision of Professor Paul Embrechts.