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

2020/04/23 by Bouchard, Bruno, Tan, Xiaolu · 1 citation
#FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2004.11105

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 only concave in space and non-increasing in time, in the sense of Dupire.

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