On the martingale selection problem and its connection to arbitrage theory

Given a collection of random set, the martingale selection problem consists in finding a selection of these sets and a probability measure with respect to which the selection is a martingale. We solve this problem in a pointwise framework, i.e. in absence of a reference probability and in discrete time. In a second part we show how the solution of this problem is strongly connected with arbitrage theory and show how to derive fundamental theorems of asset pricing in various context, from frictionless markets to general transaction costs. Joint work with Mario Sikic.