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arXiv · 1512.01698

Purely pathwise probability-free Ito integral

Vladimir Vovk
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Abstract

This paper gives several simple constructions of the pathwise Ito integral $\int_0^tϕdω$ for an integrand $ϕ$ and a price path $ω$ as integrator, with $ϕ$ and $ω$ satisfying various topological and analytical conditions. The definitions are purely pathwise in that neither $ϕ$ nor $ω$ are assumed to be paths of stochastic processes, and the Ito integral exists almost surely in a non-probabilistic financial sense. For example, one of the results shows the existence of $\int_0^tϕdω$ for a cadlag integrand $ϕ$ and a cadlag integrator $ω$ with jumps bounded in a predictable manner.

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Vladimir Vovk. 2016-06-07. Purely pathwise probability-free Ito integral. https://arxiv.org/abs/1512.01698

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