The impact of a partial borrowing limit on financial decisions

We consider a consumption, investment, life insurance, and retirement decision problem in which an economic agent is allowed to borrow against only a part of future income. The closed-form solution is attained by applying a dual approach that directly imposes the conditions for the borrowing limit on a dual value function. We provide analytic comparative statics for optimal strategies with rigorous proofs. It is confirmed that a more stringent borrowing limit leads to less consumption and less life insurance purchase. However, even with a tighter borrowing limit, an agent with weak incentive to retire can invest more when the wealth level is high enough. We also show that a more stringent borrowing limit can delay or hasten the optimal retirement timing depending on the agent's current wealth level.