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On the quadratic variation of the model-free price paths with jumps

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  • Lesiba Ch. Galane
  • Rafa{l} M. {L}ochowski
  • Farai J. Mhlanga

Abstract

We prove that the model-free typical (in the sense of Vovk) c\`adl\`ag price paths with mildly restricted downward jumps possess quadratic variation which does not depend on the specific sequence of partitions as long as these partitions are obtained from stopping times such that the oscillations of a path on the consecutive (half-open on the right) intervals of these partitions tend (in a specified sense) to 0. Finally, we also define quasi-explicit, partition independent quantities which tend to this quadratic variation.

Suggested Citation

  • Lesiba Ch. Galane & Rafa{l} M. {L}ochowski & Farai J. Mhlanga, 2017. "On the quadratic variation of the model-free price paths with jumps," Papers 1710.07894, arXiv.org, revised May 2018.
    • Handle: RePEc:arx:papers:1710.07894
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    References listed on IDEAS

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    1. Rafa{l} M. {L}ochowski & Nicolas Perkowski & David J. Promel, 2016. "A superhedging approach to stochastic integration," Papers 1609.02349, arXiv.org, revised Sep 2017.
    2. Vladimir Vovk, 2012. "Continuous-time trading and the emergence of probability," Finance and Stochastics, Springer, vol. 16(4), pages 561-609, October.
    3. Łochowski, Rafał M. & Miłoś, Piotr, 2013. "On truncated variation, upward truncated variation and downward truncated variation for diffusions," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 446-474.
    4. Nicolas Perkowski & David J. Promel, 2013. "Pathwise stochastic integrals for model free finance," Papers 1311.6187, arXiv.org, revised Jun 2016.
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