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

Bruno Bouchard () and Xiaolu Tan ()
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Bruno Bouchard: Université Paris-Dauphine, PSL, CNRS
Xiaolu Tan: The Chinese University of Hong Kong

Finance and Stochastics, 2021, vol. 25, issue 3, No 3, 505-528

Abstract: Abstract 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 concave in space and nonincreasing in time, in the sense of Dupire.

Keywords: Optional decomposition; Super-hedging duality; Functional Itô formula; Processes with jumps; 60G44; 93E20; 60H05 (search for similar items in EconPapers)
JEL-codes: C61 G13 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00780-021-00458-3

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