Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/312327 
Year of Publication: 
2022
Citation: 
[Journal:] Finance and Stochastics [ISSN:] 1432-1122 [Volume:] 26 [Issue:] 4 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2022 [Pages:] 927-982
Publisher: 
Springer, Berlin, Heidelberg
Abstract: 
A standing assumption in the literature on proportional transaction costs is efficient friction. Together with robust no free lunch with vanishing risk, it rules out strategies of infinite variation as they usually appear in frictionless markets. In this paper, we show how the models with and without transaction costs can be unified. The bid and ask prices of a risky asset are given by càdlàg processes which are locally bounded from below and may coincide at some points. In a first step, we show that if the bid–ask model satisfies "no unbounded profit with bounded risk" for simple strategies, then there exists a semimartingale lying between the bid and ask price processes. In a second step, under the additional assumption that the zeros of the bid–ask spread are either starting points of an excursion away from zero or inner points from the right, we show that for every bounded predictable strategy specifying the amount of risky assets, the semimartingale can be used to construct the corresponding self-financing risk-free position in a consistent way. Finally, the set of most general strategies is introduced, which also provides a new view on the frictionless case.
Subjects: 
Proportional transaction costs
No unbounded profit with bounded risk
Strategies of infinite variation
Semimartingales
Stochastic integration
JEL: 
G12
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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