We investigate financial markets under model risk caused by uncertain
volatilities. For this purpose we consider a financial market that features
volatility uncertainty. To have a mathematical consistent framework we use the
notion of G-expectation and its corresponding G-Brownian motion recently
introduced by Peng (2007). Our financial market consists of a riskless asset
and a risky stock with price process modeled by a geometric G-Brownian motion.
We adapt the notion of arbitrage to this more complex situation and consider
stock price dynamics which exclude arbitrage opportunities.