Lithuanian Mathematical Journal

, Volume 58, Issue 2, pp 141–156 | Cite as

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

  • Lesiba Charles Galane
  • Rafał Marcin Łochowski
  • Farai Julius Mhlanga
Article
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Abstract

We prove that the model-free typical (in the sense of Vovk) càdlàg 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 that tend to this quadratic variation.

Keywords

Vovk’s outer measure càdlàg price paths Lebesque partition quadratic variation truncated variation 

MSC

60H05 91G99 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Lesiba Charles Galane
    • 1
  • Rafał Marcin Łochowski
    • 2
  • Farai Julius Mhlanga
    • 1
  1. 1.Department of Mathematics and Applied MathematicsUniversity of LimpopoSovengaSouth Africa
  2. 2.Department of Mathematics and Mathematical Economics, Warsaw School of EconomicsWarszawaPoland

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