Quasi-sure essential supremum and applications to finance

Laurence Carassus ()
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Laurence Carassus: Université Paris-Saclay

Finance and Stochastics, 2025, vol. 29, issue 1, No 6, 219-260

Abstract: Abstract When uncertainty is modelled by a non-dominated and non-compact set of probability measures, a notion of essential supremum for a family of real-valued functions is developed in terms of upper semi-analytic functions. We show how the properties postulated on the initial functions carry over to their quasi-sure essential supremum. We propose various applications to financial problems with frictions. We analyse superreplication and prove a bidual characterisation of the superhedging cost. We also study a weak no-arbitrage condition called absence of instantaneous profit ( AIP $\mathrm{AIP}$ ) under which prices are finite. This requires new results on the aggregation of quasi-sure statements.

Keywords: Quasi-sure essential supremum; Model uncertainty; Non-dominated model; Market with frictions; Superreplication; Absence of instantaneous profit ( AIP $\mathrm{AIP}$ ); 28B20; 60A10; 91G20; 91G80; 93E20 (search for similar items in EconPapers)
JEL-codes: C61 C65 G12 G13 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00780-024-00553-1

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