Abstract
The problem of robust hedging requires to solve the problem of superhedging under a nondominated family of singular measures. Recent progress was achieved by van Handel, Neufeld, and Nutz. We show that the dual formulation of this problem is valid in a context suitable for martingale optimal transportation or, more generally, for optimal transportation under controlled stochastic dynamics.
Highlights
An important attention is focused on the problem of robust superhedging in the recent literature
Motivated by the original works of Avellaneda [1] and Lyons [2], the first general formulation of this problem was introduced by Denis and Martini [4] by considering the hedging problem under a nondominated family of probability measures on the canonical space of continuous trajectories
By using the notion of measurable analyticity, van Handel and Nutz [11] and Neufeld and Nutz [9] extended the previous results to general measurable claims by introducing some conditions that the non-dominated family of singular measures must satisfy
Summary
An important attention is focused on the problem of robust superhedging in the recent literature. The main objective of this paper is to extend the approach of Neufeld and Nutz [9] so as to introduce some specific additional constraints on the family of probability measures, and to weaken the integrability condition on the random variables of interest. Such an extension is crucially needed in the recent problem of martingale transportation problem [5, 6], where the superhedging problem allows for the static trading of any Vanilla payoff in addition to the dynamic trading of the underlying risky asset.
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