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A quasi-sure optional decomposition and super-hedging result on the Skorokhod space

Bouchard, Bruno; Tan, Xiaolu (2020), A quasi-sure optional decomposition and super-hedging result on the Skorokhod space. https://basepub.dauphine.fr/handle/123456789/20680

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Type
Document de travail / Working paper
External document link
https://arxiv.org/abs/2004.11105
Date
2020
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
16
Metadata
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Author(s)
Bouchard, Bruno
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Tan, Xiaolu
Department of mathematics, Chinese University of Hong Kong
Abstract (EN)
We prove a robust super-hedging duality result for path-dependent options on assets with jumps, in a continuous time setting. It requires that the collection of martingale measures is rich enough and that the payoff function satisfies some continuity property. It is a by-product of a quasi-sure version of the optional decomposition theorem, which can also be viewed as a functional version of Itô’s Lemma, that applies to non-smooth functionals (of càdlàg processes) which are only concave in space and non-increasing in time, in the sense of Dupire.
Subjects / Keywords
Skorokhod space; super-hedging result