Optimal investment, consumption and retirement decision with disutility and borrowing constraints

In this paper we consider a general consumption, portfolio and retirement optimization problem in which a working investor has borrowing constraints. Closed-form solutions are obtained for the utility maximization problems, and numerical procedures are given for the general utility function under borrowing constraints. Moreover, we apply the results to the special utility function, the constant relative risk-aversion utility function, and the numerical results suggest that the restriction to borrowing future labor income makes the investor retire at a lower critical wealth level than in the case of no borrowing constraints.