Purely pathwise probability-free Ito integral

Author
V. Vovk
Department of Computer Science, Royal Holloway, University of London
Abstract
This paper gives a simple construction of the pathwise Ito integral $\int_0^t\phi d\omega$ for an integrand $\phi$ and an integrator $\omega$ satisfying various topological and analytical conditions. The definition is purely pathwise in that neither $\phi$ nor $\omega$ are assumed to be paths of processes, and the Ito integral exists almost surely in a non-probabilistic finance-theoretic sense. For example, one of the results shows the existence of $\int_0^t\phi d\omega$ for a cadlag integrand $\phi$ and a cadlag integrator $\omega$ with jumps bounded in a predictable manner.
Keywords
box-counting dimension; Ito integral; Ito’s formula; pathwise integration; quadratic variation
DOI
doi:10.15330/ms.46.1.96-110
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Pages
96-110
Volume
46
Issue
1
Year
2016
Journal
Matematychni Studii
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