On the quasi-sure superhedging duality with frictions

We prove the superhedging duality for a discrete-time financial market with proportional transaction costs under model uncertainty. Frictions are modelled through solvency cones as in the original model of Kabanov (Finance Stoch. 3:237-248, 1999) adapted to the quasi-sure setup of Bouchard and Nutz (Ann. Appl. Probab. 25:823-859, 2015). Our approach allows removing the restrictive assumption of no arbitrage of the second kind considered in Bouchard et al. (Math. Finance 29:837-860, 2019) and showing the duality under the more natural condition of strict no arbitrage. In addition, we extend the results to models with portfolio constraints.