  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. Due to volatility
uncertainty the market is not complete any more. We establish the interval of
no-arbitrage prices for general European contingent claims and deduce explicit
results in a Markovian setting.
