A unified framework for robust modelling of financial markets in discrete time

Jan Obłój () and Johannes Wiesel ()
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Jan Obłój: University of Oxford
Johannes Wiesel: Columbia University

Finance and Stochastics, 2021, vol. 25, issue 3, No 1, 427-468

Abstract: Abstract We unify and establish equivalence between the pathwise and the quasi-sure approaches to robust modelling of financial markets in finite discrete time. In particular, we prove a fundamental theorem of asset pricing and a superhedging theorem which encompass the formulations of Bouchard and Nutz [12] and Burzoni et al. [13]. In bringing the two streams of literature together, we examine and compare their many different notions of arbitrage. We also clarify the relation between robust and classical ℙ-specific results. Furthermore, we prove when a superhedging property with respect to the set of martingale measures supported on a set Ω $\Omega $ of paths may be extended to a pathwise superhedging on Ω $\Omega $ without changing the superhedging price.

Keywords: Robust pricing and hedging; Superhedging; Model-independent arbitrage; Dynamic programming principle; 91G20; 60G42 (search for similar items in EconPapers)
JEL-codes: C61 C65 G12 G13 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s00780-021-00454-7

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