Pathwise Integration and functional calculus for paths with finite quadratic variation

Ananova, Anna

doi:10.25560/66091

2018

DOI: 10.25560/66091

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Pathwise Integration and functional calculus for paths with finite quadratic variation

Anna Ananova¹

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2023

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A càdlàg rough path foundation for robust finance

Allan,

Liu,

Prömel

2023

Finance Stoch

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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.

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A càdlàg rough path foundation for robust finance

Allan,

Liu,

Prömel

2023

Finance Stoch

View full text Add to dashboard Cite

show abstract

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Pathwise Integration and functional calculus for paths with finite quadratic variation

Cited by 1 publication

References 16 publications

A càdlàg rough path foundation for robust finance

A càdlàg rough path foundation for robust finance

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