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Purely pathwise probability-free Ito integral

2015/12/05 by Vovk, Vladimir
#60H05 #91G99 #FOS: Economics and business #Mathematical Finance (q-fin.MF)

paper · doi:10.48550/arxiv.1512.01698

Abstract

This paper gives several simple constructions of the pathwise Ito integral ∫0tϕdω 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 ∫0tϕdω for a cadlag integrand ϕ and a cadlag integrator ω with jumps bounded in a predictable manner.

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