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Pathwise superhedging on prediction sets

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Abstract

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

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Acknowledgement

Part of this research was carried out while the first author was visiting the Shanghai Advanced Institute of Finance and the School of Mathematical Sciences at the Shanghai Jiao Tong University in China, and he would like to thank Samuel Drapeau for his hospitality. This author also acknowledges financial support by the Vienna Science and Technology Fund (WWTF) through project VRG17-005 and by the Austrian Science Fund (FWF) under grant Y00782. The third author gratefully acknowledges the financial support by the NAP Grant and by the Swiss National Foundation Grant SNF 200020\(\_\)172815.

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Authors and Affiliations

  1. Department of Mathematics, University of Vienna, Vienna, Austria

    Daniel Bartl

  2. Department of Mathematics and Statistics, University of Konstanz, Konstanz, Germany

    Michael Kupper

  3. Division of Mathematical Sciences, NTU Singapore, Singapore, Singapore

    Ariel Neufeld

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  1. Daniel Bartl
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  2. Michael Kupper
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  3. Ariel Neufeld
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Correspondence to Ariel Neufeld.

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Bartl, D., Kupper, M. & Neufeld, A. Pathwise superhedging on prediction sets. Finance Stoch 24, 215–248 (2020). https://doi.org/10.1007/s00780-019-00412-4

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