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 language | English |
|---|---|
| Pages (from-to) | 96-110 |
| Number of pages | 15 |
| Journal | Matematychni Studii |
| Volume | 46 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2016 |
Keywords
- Box-counting dimension; Ito integral; Ito’s formula; pathwise integration; quadratic variation