## The Annals of Applied Probability

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

### Model-free superhedging duality

Matteo Burzoni, Marco Frittelli, and Marco Maggis

#### 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**

Received: June 2015

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

**Subjects**

Primary: 60B05: Probability measures on topological spaces 60G42: Martingales with discrete parameter 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05] 28B20: Set-valued set functions and measures; integration of set-valued functions; measurable selections [See also 26E25, 54C60, 54C65, 91B14] 46A20: Duality theory 91B70: Stochastic models 91B24: Price theory and market structure

**Keywords**

Superhedging theorem model independent market model uncertainty robust duality finite support martingale measure analytic sets

#### 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