  By the calculus of Peng's G-sublinear expectation and G-Brownian motion on a
sublinear expectation space $(\Omega, {\cal H}, \hat{\mathbb{E}})$, we first
set up an optimality principle of stochastic control problem. Then we
investigate an optimal consumption and portfolio decision with a volatility
ambiguity by the derived verification theorem. Next the two-fund separation
theorem is explicitly obtained. And an illustrative example is provided.
