The effects of pre-/post-retirement borrowing constraints on optimal consumption, investment, and retirement

In this paper, we explore an optimization problem in which a working agent with an option to retire wants to maximize her expected lifetime utility. The agent receives labor (or annuity) income before/after retirement and experiences dis-utility due to labor. Additionally, the agent can partially borrow against her future income before/after retirement. We demonstrate that when pre-retirement borrowing constraints are strict, the agent retires early, while strong post-retirement borrowing constraints result in a late retirement. Our numerical results reveal that the retirement threshold level changes with varying interest rates, with an increase in interest rates leading to a general decrease in the retirement threshold level. However, in certain cases with borrowing constraints, the declining effects of pre-/post-retirement discounted income strongly influence the retirement decision as the interest rate increases. Additionally, our findings indicate that the impact of the volatility of the risky asset and the interest rate on the retirement wealth level varies. Specifically, at low interest rates, higher volatility is associated with an increased retirement wealth level, while at high interest rates, lower volatility results in a marginal increase in the retirement wealth level. These findings suggest a diminishing influence of volatility on the retirement wealth level as interest rates rise.