Asymptotics of the truncated variation of model-free price paths and semimartingales with jumps

Abstract

We prove that typical (in the model-free finance setting) price paths with jumps may be uniformly approximated with accuracy $c>0$ by paths whose total variation is of order $1/c.$ A more precise result is obtained for semimartingales with jumps.

I found a gap in the proof of Theorem 1

References in corpus (3)

• The Play Operator, the Truncated Variation and the Generalisation of the Jordan Decomposition
• Riemann-Stieltjes integrals driven by irregular signals in Banach spaces and rate-independent characteristics of their irregularity
• Integration of rough paths - the truncated variation approach