  We consider an optimal investment and consumption problem for a Black-Scholes
financial market with stochastic volatility and unknown stock appreciation
rate. The volatility parameter is driven by an external economic factor modeled
as a diffusion process of Ornstein-Uhlenbeck type with unknown drift. We use
the dynamical programming approach and find an optimal financial strategy which
depends on the drift parameter. To estimate the drift coefficient we observe
the economic factor $Y$ in an interval $[0,T_0]$ for fixed $T_0>0$, and use
sequential estimation. We show, that the consumption and investment strategy
calculated through this sequential procedure is $\delta$-optimal.
