The Annals of Applied Probability

Model-free superhedging duality

Matteo Burzoni, Marco Frittelli, and Marco Maggis

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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


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