The impact of a partial borrowing limit on financial decisions

Byung Hwa Lim and Minsuk Kwak

Quantitative Finance, 2019, vol. 19, issue 5, 859-883

Abstract: 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.

Date: 2019
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DOI: 10.1080/14697688.2018.1526395

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