# Coherence Of Game-theoretic Brownian Motion

This is perhaps the most important open question in the area of continuous-time game-theoretic probability. It is stated precisely in the last section of [Vovk 2008] (the second question). A positive answer to this question would lead to simpler and more intuitive framework for continuous-time game-theoretic probability. A negative answer would also be of great interest, providing a counter-intuitive phenomenon akin to the Banach – Tarski paradox.

- Vladimir Vovk. Game-theoretic Brownian motion. arXiv technical report, January 2008.