Before revision:  In the analysis, there is no technical assumption (except a natural one) on the model parameters. We also prove an asymptotic expansion result for small transaction costs .
After revision:  We find an explicit characterization of model parameters for the well-posedness of the problem, and show that the problem is well-posed if and only if there exists a shadow price process. Finally, we describe how the investor's optimal strategy is affected by the additional opportunity of trading the liquid risky asset, compared to the simpler model with one bond and one illiquid risky asset .