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Unemployment Risks and Optimal Retirement in an Incomplete Market

Alain Bensoussan¹; Bong-Gyu Jang²; Seyoung Park³

¹ Naveen Jindal School of Management, University of Texas at Dallas, Richardson, Texas 75080; and Department of Systems Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong · ² Department of Industrial and Management Engineering, Pohang University of Science and Technology, Pohang, Korea 37673 · ³ Department of Industrial and Management Engineering, Pohang University of Science and Technology, Pohang, Korea 37673; and Risk Management Institute, National University of Singapore, Singapore 119613

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 postretirement leisure. Finally, we find that our model explains a countercyclical pattern of the number of unemployed job leavers.

DOI

10.1287/opre.2016.1503

Volume

64 (4)

Pages

1015-1032

Language

en

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Sources

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