We study an optimal investment/consumption problem in a model economy capturing market and credit risk dependencies. Stochastic factors drive both the default intensity and the volatility of the stocks in the portfolio. Using the martingale approach, we analyze the recursive system of nonlinear Hamilton-Jacobi-Bellman equations associated with the dual problem. We transform such a system into an equivalent system of semilinear PDEs, for which we establish existence and uniqueness of a bounded global classical solution. We obtain explicit representations for the optimal strategy, consumption path, and wealth process, in terms of the solution to the recursive system of semilinear PDEs. We numerically analyze the sensitivity of the optimal investment strategies to risk aversion, default risk, and volatility.