On the quasi-sure superhedging duality with frictions

Abstract

We prove the superhedging duality for a discrete-time financial market with proportional transaction costs under model uncertainty. Frictions are modeled through solvency cones as in the original model of Kabanov [1999] adapted to the quasi-sure setup of Bouchard and Nutz [2015]. Our approach allows to remove the restrictive assumption of No Arbitrage of the Second Kind considered in Bouchard et al. [2017] and to show the duality under the more natural condition of No Strict Arbitrage. In addition, we extend the results to models with portfolio constraints.

Utility maximization with proportional transaction costs under model uncertainty

“…(iii) After the completion of our paper, Bayraktar and Burzoni [5] provided a generalization of the randomization approach in [14] and proved a pricing-hedging duality under a weaker no-arbitrage condition than the NA2(P) condition. Their generalized randomization approach should also allow to study the above utility maximization problem under the weak no-arbitrage condition.…”

“…Consequently, the unpleasant mathematical obstacles caused by trading fees can be hidden in an enlarged space with additional randomness and some techniques in the literature of robust hedging and utility maximization in frictionless models can be modified and adopted. It is worth noting that by applying the randomization approach in [14] but with a different and more involved definition of family of probability measures on the enlarged space, [5] recently established a super-replication duality with transaction cost under a weaker no-arbitrage condition.…”