Unemployment Risks and Optimal Retirement in an Incomplete Market

Operations Research, Forthcoming

Posted: 20 Jan 2013 Last revised: 6 Mar 2016

See all articles by Alain Bensoussan

Alain Bensoussan

University of Texas at Dallas - Naveen Jindal School of Management; Hong Kong Polytechnic University - Faculty of Business; Ajou University

Bong-Gyu Jang

Pohang University of Science and Technology (POSTECH)

Seyoung Park

Nottingham University Business School

Date Written: January 14, 2013

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 the 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 a relatively higher stock holdings for the poor. We also analyze the sensitivity of an individual's optimal behaviors in changing her wealth level, investment opportunity, and the magnitude of preference for post-retirement leisure. Finally, we find our model explains a procyclical pattern of the number of unemployed job leavers.

Keywords: unemployment risk, optimal retirement, optimal investment, portfolio theory, dynamic programming, convex duality

JEL Classification: C61, G11, J64

Suggested Citation

Bensoussan, Alain and Jang, Bong-Gyu and Park, Seyoung, Unemployment Risks and Optimal Retirement in an Incomplete Market (January 14, 2013). Operations Research, Forthcoming . Available at SSRN: https://ssrn.com/abstract=2203594 or http://dx.doi.org/10.2139/ssrn.2203594

Alain Bensoussan

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 West Campbell Rd
SM 30
Richardson, TX 75080-3021
United States
9728836117 (Phone)

HOME PAGE: http://www.utdallas.edu/~axb046100/

Hong Kong Polytechnic University - Faculty of Business

Dept SEEM
Systems Engr * Engr Mgmt
Hong Kong, Hong Kong
China

Ajou University ( email )

Ajou
France

Bong-Gyu Jang (Contact Author)

Pohang University of Science and Technology (POSTECH) ( email )

77 Cheongam-ro
Pohang
Korea, Republic of (South Korea)

Seyoung Park

Nottingham University Business School ( email )

Nottingham University Business School
Jubilee Campus
Nottingham
United Kingdom
+44-7927-494518 (Phone)

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