## The Annals of Applied Probability

### Model-free superhedging duality

#### Abstract

In a model-free discrete time financial market, we prove the superhedging duality theorem, where trading is allowed with dynamic and semistatic strategies. We also show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path $\omega \in \Omega$, might be strictly greater than the upper bound of the no-arbitrage prices. We therefore characterize the subset of trajectories on which this duality gap disappears and prove that it is an analytic set.

#### Article information

Source
Ann. Appl. Probab., Volume 27, Number 3 (2017), 1452-1477.

Dates
Revised: May 2016
First available in Project Euclid: 19 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1500451228

Digital Object Identifier
doi:10.1214/16-AAP1235

Mathematical Reviews number (MathSciNet)
MR3678476

Zentralblatt MATH identifier
1370.60004

#### Citation

Burzoni, Matteo; Frittelli, Marco; Maggis, Marco. Model-free superhedging duality. Ann. Appl. Probab. 27 (2017), no. 3, 1452--1477. doi:10.1214/16-AAP1235. https://projecteuclid.org/euclid.aoap/1500451228

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