Pathwise superhedging on prediction sets

Daniel Bartl (), Michael Kupper () and Ariel Neufeld ()
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Daniel Bartl: University of Vienna
Michael Kupper: University of Konstanz
Ariel Neufeld: NTU Singapore

Finance and Stochastics, 2020, vol. 24, issue 1, No 6, 215-248

Abstract: Abstract In this paper, we provide a pricing–hedging duality for the model-independent superhedging price with respect to a prediction set Ξ⊆C[0,T]$\Xi \subseteq C[0,T]$, where the superhedging property needs to hold pathwise, but only for paths lying in Ξ$\Xi $. For any Borel-measurable claim ξ$\xi $ bounded from below, the superhedging price coincides with the supremum over all pricing functionals EQ[ξ]$\mathbb{E}_{\mathbb{Q}}[ \xi ]$ with respect to martingale measures ℚ concentrated on the prediction set Ξ$\Xi $. This allows us to include beliefs about future paths of the price process expressed by the set Ξ$\Xi $, while eliminating all those which are seen as impossible. Moreover, we provide several examples to justify our setup.

Keywords: Model-independent superhedging; Pricing–hedging duality; Modelling beliefs; 91B24; 91G20; 60G44 (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (14)

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DOI: 10.1007/s00780-019-00412-4

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