On the quadratic variation of the model-free price paths with jumps
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.
KeywordsVovk’s outer measure càdlàg price paths Lebesque partition quadratic variation truncated variation
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