  We study an optimal investment/consumption problem in a model capturing
market and credit risk dependencies. Stochastic factors drive both the default
intensity and the volatility of the stocks in the portfolio. We use the
martingale approach and 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 semi-linear 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 semi-linear PDEs. We numerically analyze the sensitivity of the
optimal investment strategies to risk aversion, default risk and volatility.
