An optimal consumption and investment problem with quadratic utility and subsistence consumption constraints: a dynamic programming approach

Abstract

In this paper, we analyze the optimal consumption and investment problem of an agent who has a quadratic-type utility function and faces a subsistence consumption constraint. We use the dynamic programming method to solve the optimization problem in continuous-time. We further provide the sufficient conditions for the optimization problem to be well-defined.

Keywords

• portfolio selection
• quadratic utility
• subsistence consumption constraints
• dynamic programming method