A càdlàg rough path foundation for robust finance

Andrew L. Allan (), Chong Liu () and David J. Prömel ()
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Andrew L. Allan: Durham University
Chong Liu: ShanghaiTech University
David J. Prömel: University of Mannheim

Finance and Stochastics, 2024, vol. 28, issue 1, No 6, 215-257

Abstract: Abstract Using rough path theory, we provide a pathwise foundation for stochastic Itô integration which covers most commonly applied trading strategies and mathematical models of financial markets, including those under Knightian uncertainty. To this end, we introduce the so-called property (RIE) for càdlàg paths, which is shown to imply the existence of a càdlàg rough path and of quadratic variation in the sense of Föllmer. We prove that the corresponding rough integrals exist as limits of left-point Riemann sums along a suitable sequence of partitions. This allows one to treat integrands of non-gradient type and gives access to the powerful stability estimates of rough path theory. Additionally, we verify that (path-dependent) functionally generated trading strategies and Cover’s universal portfolio are admissible integrands, and that property (RIE) is satisfied by both (Young) semimartingales and typical price paths.

Keywords: Föllmer integration; Model uncertainty; Semimartingale; Pathwise integration; Rough path; Functionally generated portfolios; Universal portfolio; 91G80; 60L20; 60G44 (search for similar items in EconPapers)
JEL-codes: C50 G10 G11 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00780-023-00522-0

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