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Unemployment Risks and Optimal Retirement in an Incomplete Market

Author

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  • Alain Bensoussan

    (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)

  • Bong-Gyu Jang

    (Department of Industrial and Management Engineering, Pohang University of Science and Technology, Pohang, Korea 37673)

  • Seyoung Park

    (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)

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

Suggested Citation

  • Alain Bensoussan & Bong-Gyu Jang & Seyoung Park, 2016. "Unemployment Risks and Optimal Retirement in an Incomplete Market," Operations Research, INFORMS, vol. 64(4), pages 1015-1032, August.
    • Handle: RePEc:inm:oropre:v:64:y:2016:i:4:p:1015-1032
    DOI: 10.1287/opre.2016.1503
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    1. Elmendorf, Douglas W & Kimball, Miles S, 2000. "Taxation of Labor Income and the Demand for Risky Assets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(3), pages 801-833, August.
    2. Dybvig, Philip H. & Liu, Hong, 2010. "Lifetime consumption and investment: Retirement and constrained borrowing," Journal of Economic Theory, Elsevier, vol. 145(3), pages 885-907, May.
    3. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-987, December.
    4. Luca Benzoni & Pierre Collin‐Dufresne & Robert S. Goldstein, 2007. "Portfolio Choice over the Life‐Cycle when the Stock and Labor Markets Are Cointegrated," Journal of Finance, American Finance Association, vol. 62(5), pages 2123-2167, October.
    5. C. L. Marston & B. M. Craven, 1998. "A survey of corporate perceptions of short-termism among analysts and fund managers," The European Journal of Finance, Taylor & Francis Journals, vol. 4(3), pages 233-256.
    6. Lynch, Anthony W. & Tan, Sinan, 2011. "Labor income dynamics at business-cycle frequencies: Implications for portfolio choice," Journal of Financial Economics, Elsevier, vol. 101(2), pages 333-359, August.
    7. George Chacko & Luis M. Viceira, 2005. "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets," The Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1369-1402.
    8. Andrew Ang & Geert Bekaert, 2002. "International Asset Allocation With Regime Shifts," The Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1137-1187.
    9. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    10. Luis M. Viceira, 2001. "Optimal Portfolio Choice for Long‐Horizon Investors with Nontradable Labor Income," Journal of Finance, American Finance Association, vol. 56(2), pages 433-470, April.
    11. Valery Polkovnichenko, 2007. "Life-Cycle Portfolio Choice with Additive Habit Formation Preferences and Uninsurable Labor Income Risk," The Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 83-124, January.
    12. Henderson, Vicky, 2005. "Explicit solutions to an optimal portfolio choice problem with stochastic income," Journal of Economic Dynamics and Control, Elsevier, vol. 29(7), pages 1237-1266, July.
    13. Hyeng Keun Koo, 1998. "Consumption and Portfolio Selection with Labor Income: A Continuous Time Approach," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 49-65, January.
    14. He, Hua & Pearson, Neil D., 1991. "Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case," Journal of Economic Theory, Elsevier, vol. 54(2), pages 259-304, August.
    15. Milton Friedman, 1957. "Introduction to "A Theory of the Consumption Function"," NBER Chapters, in: A Theory of the Consumption Function, pages 1-6, National Bureau of Economic Research, Inc.
    16. Svensson, Lars E. O. & Werner, Ingrid M., 1993. "Nontraded assets in incomplete markets : Pricing and portfolio choice," European Economic Review, Elsevier, vol. 37(5), pages 1149-1168, June.
    17. Hua He & Neil D. Pearson, 1991. "Consumption and Portfolio Policies With Incomplete Markets and Short‐Sale Constraints: the Finite‐Dimensional Case1," Mathematical Finance, Wiley Blackwell, vol. 1(3), pages 1-10, July.
    18. Alex Edmans, 2009. "Blockholder Trading, Market Efficiency, and Managerial Myopia," Journal of Finance, American Finance Association, vol. 64(6), pages 2481-2513, December.
    19. Gruber, Jonathan, 1997. "The Consumption Smoothing Benefits of Unemployment Insurance," American Economic Review, American Economic Association, vol. 87(1), pages 192-205, March.
    20. Joao F. Cocco, 2005. "Consumption and Portfolio Choice over the Life Cycle," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 491-533.
    21. Farhi, Emmanuel & Panageas, Stavros, 2007. "Saving and investing for early retirement: A theoretical analysis," Journal of Financial Economics, Elsevier, vol. 83(1), pages 87-121, January.
    22. Milton Friedman, 1957. "A Theory of the Consumption Function," NBER Books, National Bureau of Economic Research, Inc, number frie57-1.
    23. Bodie, Zvi & Merton, Robert C. & Samuelson, William F., 1992. "Labor supply flexibility and portfolio choice in a life cycle model," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 427-449.
    24. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    25. Bong‐Gyu Jang & Hyeng Keun Koo & Hong Liu & Mark Loewenstein, 2007. "Liquidity Premia and Transaction Costs," Journal of Finance, American Finance Association, vol. 62(5), pages 2329-2366, October.
    26. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-161.
    27. Christopher D. Carroll, 1992. "The Buffer-Stock Theory of Saving: Some Macroeconomic Evidence," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 23(2), pages 61-156.
    28. Jang, Bong-Gyu & Park, Seyoung & Rhee, Yuna, 2013. "Optimal retirement with unemployment risks," Journal of Banking & Finance, Elsevier, vol. 37(9), pages 3585-3604.
    29. Heaton, John & Lucas, Deborah, 1997. "Market Frictions, Savings Behavior, And Portfolio Choice," Macroeconomic Dynamics, Cambridge University Press, vol. 1(1), pages 76-101, January.
    30. Jessica A. Wachter & Motohiro Yogo, 2010. "Why Do Household Portfolio Shares Rise in Wealth?," The Review of Financial Studies, Society for Financial Studies, vol. 23(11), pages 3929-3965, November.
    31. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," The Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
    32. Keppo, Jussi & Meng, Xu & Sullivan, Michael G., 2007. "A computational scheme for the optimal strategy in an incomplete market," Journal of Economic Dynamics and Control, Elsevier, vol. 31(11), pages 3591-3613, November.
    33. Lucie Teplå, 2000. "Optimal Hedging and Valuation of Nontraded Assets," Review of Finance, European Finance Association, vol. 4(3), pages 231-251.
    34. Antonios Sangvinatsos & Jessica A. Wachter, 2005. "Does the Failure of the Expectations Hypothesis Matter for Long‐Term Investors?," Journal of Finance, American Finance Association, vol. 60(1), pages 179-230, February.
    35. John Heaton & Deborah Lucas, 2000. "Portfolio Choice and Asset Prices: The Importance of Entrepreneurial Risk," Journal of Finance, American Finance Association, vol. 55(3), pages 1163-1198, June.
    36. Duffie, Darrell & Fleming, Wendell & Soner, H. Mete & Zariphopoulou, Thaleia, 1997. "Hedging in incomplete markets with HARA utility," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 753-782, May.
    37. Bodie, Zvi & Detemple, Jerome B. & Otruba, Susanne & Walter, Stephan, 2004. "Optimal consumption-portfolio choices and retirement planning," Journal of Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1115-1148, March.
    38. Gormley, Todd & Liu, Hong & Zhou, Guofu, 2010. "Limited participation and consumption-saving puzzles: A simple explanation and the role of insurance," Journal of Financial Economics, Elsevier, vol. 96(2), pages 331-344, May.
    39. Malley, James R & Moutos, Thomas, 1996. "Unemployment and Consumption," Oxford Economic Papers, Oxford University Press, vol. 48(4), pages 584-600, October.
    40. Kyoung Jin Choi & Gyoocheol Shim & Yong Hyun Shin, 2008. "Optimal Portfolio, Consumption‐Leisure And Retirement Choice Problem With Ces Utility," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 445-472, July.
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