  Model uncertainty is a type of inevitable financial risk. Mistakes on the
choice of pricing model may cause great financial losses. In this paper we
investigate financial markets with mean-volatility uncertainty. Models for
stock markets and option markets with uncertain prior distribution are
established by Peng's G-stochastic calculus. The process of stock price is
described by generalized geometric G-Brownian motion in which the mean
uncertainty may move together with or regardless of the volatility uncertainty.
On the hedging market, the upper price of an (exotic) option is derived
following the Black-Scholes-Barenblatt equation. It is interesting that the
corresponding Barenblatt equation does not depend on the risk preference of
investors and the mean-uncertainty of underlying stocks. Hence under some
appropriate sublinear expectation, neither the risk preference of investors nor
the mean-uncertainty of underlying stocks pose effects on our super and
subhedging strategies. Appropriate definitions of arbitrage for super and
sub-hedging strategies are presented such that the super and sub-hedging prices
are reasonable. Especially the condition of arbitrage for sub-hedging strategy
fills the gap of the theory of arbitrage under model uncertainty. Finally we
show that the term $K$ of finite-variance arising in the super-hedging strategy
is interpreted as the max Profit\&Loss of being short a delta-hedged option.
The ask-bid spread is in fact the accumulation of summation of the superhedging
$P\&L$ and the subhedging $P\&L $.
