Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/307069 
Year of Publication: 
2023
Citation: 
[Journal:] Finance and Stochastics [ISSN:] 1432-1122 [Volume:] 28 [Issue:] 1 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2023 [Pages:] 215-257
Publisher: 
Springer, Berlin, Heidelberg
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.
Subjects: 
Föllmer integration
Model uncertainty
Semimartingale
Pathwise integration
Rough path
Functionally generated portfolios
Universal portfolio
JEL: 
C50
G10
G11
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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