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Abstract

This paper gives a simple construction of the pathwise Ito integral ∫ ϕ dω for an integrand ϕ and an integrator ω satisfying various topological and analytical conditions. The definition is purely pathwise in that neither ϕ nor ω 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 ∫ ϕ dω for a cadlag integrand ϕ and a cadlag integrator ω with jumps bounded in a predictable manner.
Original languageEnglish
Pages (from-to)96-110
Number of pages15
JournalMatematychni Studii
Volume46
Issue number1
DOIs
Publication statusPublished - 2016

Keywords

  • Box-counting dimension; Ito integral; Ito’s formula; pathwise integration; quadratic variation

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