An optimal retirement problem with job switching and unemployment risks under subsistence consumption constraints

Qi Li, Yong Hyun Shin and Ji-Hun Yoon

Quantitative Finance, 2025, vol. 25, issue 5, 795-815

Abstract: This study presents for the first time a rigorous continuous-time optimal involuntary and voluntary retirement model that includes job-switching opportunities and subsistence consumption constraints. Two job states are allowed; $ J_1 $ J1 and $ J_2 $ J2. Job state $ J_1 $ J1 provides a higher income but less leisure time than job state $ J_2 $ J2. We examine the impacts of unemployment risk, job switching, and subsistence consumption constraints on consumption and investment decisions across three potential retirement statuses: voluntary retirement, involuntary retirement in job state $ J_1 $ J1, and involuntary retirement in job state $ J_2 $ J2. Using closed-form solutions derived from theoretical models by applying the Martingale approach and variational inequality method validated through comparative statics both analytically and numerically, we analyze how different unemployment possibilities, competitive insurance market conditions, and subsistence consumption levels influence individuals' economic decisions. Our findings indicate that subsistence consumption constraints and unemployment risk significantly reduce consumption and investment levels before voluntary retirement. Moreover, as the probability of unemployment increases, the wealth boundary for voluntary retirement decreases.

Date: 2025
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DOI: 10.1080/14697688.2025.2498395

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