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A càdlàg rough path foundation for robust finance

Allan, Andrew L.; Liu, Chong; Prömel, David J.

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Chong Liu

David J. Prömel


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.


Allan, A. L., Liu, C., & Prömel, D. J. (2024). A càdlàg rough path foundation for robust finance. Finance and Stochastics, 28(1), 215-257.

Journal Article Type Article
Acceptance Date Apr 19, 2023
Online Publication Date Nov 17, 2023
Publication Date Jan 1, 2024
Deposit Date May 2, 2023
Publicly Available Date Jan 4, 2024
Journal Finance and Stochastics
Print ISSN 0949-2984
Electronic ISSN 1432-1122
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 28
Issue 1
Pages 215-257
Keywords Semimartingale, Föllmer integration, Rough path, G11, Universal portfolio, G10, Functionally generated portfolios, 60G44, 60L20, 91G80, C50, Model uncertainty, Pathwise integration
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