Consumption-investment models with constraints

The paper examines a general investment and consumption problem for a single agent who consumes and invests in a riskless asset and a risky one. The objective is to maximize the total expected discounted utility of consumption. Trading constraints, limited borrowing, and no bankruptcy are binding, and the optimization problem is formulated as a stochastic control problem with stage and control constraints. It is shown that the value function is the unique smooth solution of the associated Hamilton-Jacobi-Bellman equation and the optimal consumption and portfolios are provided in feedback form.