Speaker: Prof Jan Obloj (Oxford) Title: Robust Finance. Part II -- Fundamental Theorems Abstract: We pursue robust approach to pricing and hedging in mathematical finance. We develop a general discrete time setting in which some underlying assets and options are available for dynamic trading and a further set of European options, possibly with varying maturities, is available for static trading. We include in our setup modelling beliefs by allowing to specify a set of paths to be considered, e.g. super-replication of a contingent claim is required only for paths falling in the given set. Our framework thus interpolates between model-independent and model-specific settings and allows to quantify the impact of making assumptions. We establish suitable FTAP and Pricing-Hedging duality results which include as special cases previous results of Acciaio et al. (2013), Bouchard and Nutz (2015), Burzoni et al. (2016) as well the Dalang-Morton-Willinger theorem. Finally, we explain how to treat further problems, such as insider trading (information quantification) or American options pricing. The talk will cover a body of results developed in collaboration with A. Aksamit, M. Burzoni, S. Deng, M. Frittelli, Z. Hou, M. Maggis, X. Tan and J. Wiesel. http://www.maths.usyd.edu.au/u/SemConf/Stochastics_Finance/seminar.html