An optimal consumption, leisure, and investment problem with an option to retire and negative wealth constraints

This paper attempts to choose the optimal consumption, leisure, investment, and voluntary retirement time under the negative wealth constraint. The Dynamic Programming method is used to derive the value function and to identify the optimal policies when the agent's utility function of consumption and leisure is given in the form of Cobb-Douglas. Finally, the effects of negative wealth constraints were discussed by examining the optimal policies that vary depending on the degree of the negative wealth constraint.