Unemployment Risks and Optimal Retirement in an Incomplete Market

Park, Seyoung; Bensoussan, Alain; Jang, Bong-Gyu

Abstract

We develop a new approach for solving the optimal retirement problem for an individual with an unhedgeable income risk. The income risk stems from a forced unemployment event, which occurs as an exponentially-distributed random shock. The optimal retirement problem is to determine an individual's optimal consumption and investment behaviors and optimal retirement time simultaneously. We introduce a new convex-duality approach for reformulating the original retirement problem and provide an iterative numerical method to solve it. Reasonably calibrated parameters say that our model can give an explanation for lower consumption and risky investment behaviors of individuals, and for relatively higher stock holdings of the poor. We also analyze the sensitivity of an individual's optimal behavior in changing her wealth level, investment opportunity, and the magnitude of preference for post-retirement leisure. Finally, we find that our model explains a counter-cyclical pattern of the number of unemployed job leavers.

Citation

Park, S., Bensoussan, A., & Jang, B.-G. (2016). Unemployment Risks and Optimal Retirement in an Incomplete Market. Operations Research, 64(4), 1015-1032. https://doi.org/10.1287/opre.2016.1503

• Journal Article Type: Article
• Acceptance Date: Mar 1, 2016
• Online Publication Date: Jun 20, 2016
• Publication Date: 2016-07
• Deposit Date: Feb 24, 2020
• Publicly Available Date: May 5, 2020
• Journal: Operations Research
• Print ISSN: 0030-364X
• Publisher: INFORMS
• Peer Reviewed: Peer Reviewed
• Volume: 64
• Issue: 4
• Pages: 1015-1032
• DOI: https://doi.org/10.1287/opre.2016.1503
• Keywords: dynamic programming/optimal control; investment; stochastic model applications
• Public URL: https://nottingham-repository.worktribe.com/output/4026041
• Publisher URL: https://pubsonline.informs.org/doi/10.1287/opre.2016.1503