In this paper, we investigate the optimal consumption and portfolio selection
problem with negative wealth constraints for an economic agent who has a
quadratic utility function of consumption and receives a constant labor income. Due
to the property of the quadratic utility function, we separate our problem into two
cases and derive the closed-form solutions for each case. We also illustrate some
numerical implications of the optimal consumption and portfolio.

• An optimal consumption and investment problem with quadratic utility and negative wealth constraints