# Volatility Of Discontinuous Price Processes

This question belongs to continuous-time game-theoretic probability. The sample space is the set of all positive right-continuous functions of time.

- Let be Taylor's function: , where . Is it true that almost surely? It is known (see [Vovk 2010]) that the answer is "yes" when is the set of all continuous functions of time. In the case of discontinuous functions, it is only known that , where [Vovk 2010].

### Bibliography

- Vladimir Vovk. Rough paths in idealized financial markets. arXiv technical report, May 2010.