Probability theory, uncertainty quantification, financial mathematics, risk management, copulas, high-dimensional problems in statistics and probability, (martingale) optimal transport, Lévy processes, numerical methods, stochastic optimization.

D. Bartl, M. Kupper, T. Lux and A. Papapantoleon, Sharpness of improved Fréchet-Hoeffding bounds: an optimal transport approach, preprint. (Download)

T. Lux and L. Rüschendorf, An optimal transport approach to Value-at-Risk bounds with partial dependence information, preprint. (Download) 

T. Lux and A. Papapantoleon, Model-free bounds on Value-at-Risk using partial dependence information, preprint, arXiv:1610.09734. (Download) 

T. Lux and A. Papapantoleon, Improved Fréchet-Hoeffding bounds on d-copulas and applications in model-free finance, forthcoming in The Annals of Applied Probability, arXiv: 1602.08894. (Download)

T. Lux, Model uncertainty, improved Fréchet-Hoeffding bounds and applications in mathematical finance, PhD Thesis, Technische Universität Berlin. (Download) 

Master project of Yan Gong, Improved Value-at-Risk bounds using extreme value theory, co-supervision with Antonis Papapantoleon (TU Berlin) and Raphael Huser (KAUST University), VUB Brussels.

Master thesis of Paulo Yanez, Copulas and their applications to multi-asset derivatives, co-supervision with Antonis Papapantoleon, TU Berlin.

Master thesis of Julia Jonczyk, Bounds on Value-at-Risk using the Rearrangement Algorithm, co-supervision with Antonis Papapantoleon, TU Berlin.

Master thesis of David Morten Schwend, Bounds for Value-at-Risk using copulas, co-supervision with Antonis Papapantoleon, TU Berlin.

Master thesis of Paul Pietzner, Cost efficient strategies in the multivariate Black-Scholes model, co-supervision with Antonis Papapantoleon, TU Berlin.