Optimal consumption and portfolio selection with negative wealth constraints,subsistence consumption constraints,and CARA utility

We consider the optimal consumption and portfolio selection problem with constant absolute risk aversion (CARA) utility. The economic agent in this model receives constant labor income, and her economic behavior is restricted on consumption and wealth, which are called the subsistence consumption constraint and the negative wealth constraint. We use the convex duality method to derive the value function and the optimal policies in closed-form solutions. Also we illustrate some numerical examples.