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Mathematics and Financial Economics

, Volume 13, Issue 2, pp 173–208 | Cite as

Borrowing constraints, effective flexibility in labor supply, and portfolio selection

  • Ho-Seok Lee
  • Gyoocheol Shim
  • Yong Hyun ShinEmail author
Article
  • 85 Downloads

Abstract

We study optimal job switching and consumption/investment policies of an economic agent under the borrowing constraints against future labor income in a continuous and infinite time horizon. The agent’s preference is given by the Cobb–Douglas utility function whose arguments are consumption and leisure, and the jobs are characterized by the trade-off between labor income and leisure. We obtain a closed-form solution to the optimization problem by using the martingale and duality method, and investigate theoretical implications of it. The most interesting finding for the optimal job switching policy is that the borrowing constraints in the financial market can decrease the effective flexibility in labor supply of the agent in the labor market. Thus, an environment of the financial market can affect an agent’s decision making in the labor market. We also show how the effects of the borrowing constraints on the optimal consumption/investment policy reinforce or compete with those of the job switching opportunities.

Keywords

Job choice Consumption/investment Borrowing constraints Effective flexibility in labor supply 

JEL Classification

J22 J24 G11 E21 

Notes

Acknowledgements

We are indebted to the anonymous referee and the Associate editor for helpful comments and suggestions. We thank the participants at the Third Asian Quantitative Finance Conference (AQFC) 2015, Chinese University of Hong Kong, Hong Kong, 2015, and International Conference on Control Theory and Mathematical Finance, Fudan University, Shanghai, 2015. An earlier version of this paper was circulated under the title: “An Optimal Job and Consumption/Investment Policy under Borrowing Constraints.”

References

  1. 1.
    Bernhardt, D., Backus, D.: Borrowing constraints, occupational choice, and labor supply. J. Labor Econ. 8, 145–173 (1990)CrossRefGoogle Scholar
  2. 2.
    Bodie, Z., Merton, R.C., Samuelson, W.F.: Labor supply flexibility and portfolio choice in a life cycle model. J. Econ. Dyn. Control 16, 427–449 (1992)CrossRefGoogle Scholar
  3. 3.
    Choi, K.J., Shim, G.: Disutility, optimal retirement, and portfolio selection. Math. Finance 16, 443–467 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Choi, K.J., Shim, G., Shin, Y.H.: Optimal portfolio, consumption-leisure and retirement choice problem with CES utility. Math. Finance 18, 445–472 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Domeij, D., Flodèn, M.: The labor-supply elasticity and borrowing constraints: why estimates are biased. Rev. Econ. Dyn. 9, 242–262 (2006)CrossRefGoogle Scholar
  6. 6.
    Dybvig, P.H., Liu, H.: Lifetime consumption and investment: retirement and constrained borrowing. J. Econ. Theory 145, 885–907 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Farhi, E., Panageas, S.: Saving and investing for early retirement: a theoretical analysis. J. Financ. Econ. 83, 87–121 (2007)CrossRefGoogle Scholar
  8. 8.
    He, H., Pagès, H.F.: Labor income, borrowing constraints, and equilibrium asset prices. Econ. Theory 3, 663–696 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Karatzas, I., Lehoczky, J.P., Sethi, S.P., Shreve, S.E.: Explicit solution of a general consumption/investment problem. Math. Oper. Res. 11, 261–294 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Karatzas, I., Shreve, S.E.: Methods of Mathematical Finance. Springer, New York (1998)CrossRefzbMATHGoogle Scholar
  11. 11.
    Karatzas, I., Wang, H.: Utility maximization with discretionary stopping. SIAM J. Control Optim. 39, 306–329 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Lim, B.H., Shin, Y.H.: Optimal investment, consumption and retirement decision with disutility and borrowing constraints. Quant. Finance 11, 1581–1592 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Merton, R.C.: Lifetime portfolio selection under uncertainty: the continuous-time case. Rev. Econ. Stat. 51, 247–257 (1969)CrossRefGoogle Scholar
  14. 14.
    Merton, R.C.: Optimum consumption and portfolio rules in a continuous-time model. J. Econ. Theory 3, 373–413 (1971)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Rendon, S.: Job search and asset accumulation under borrowing constraints. Int. Econ. Rev. 47, 233–263 (2006)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Shim, G., Shin, Y.H.: An optimal job, consumption/leisure, and investment policy. Oper. Res. Lett. 42, 145–149 (2014)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsKwangwoon UniversitySeoulRepublic of Korea
  2. 2.Department of Financial EngineeringAjou UniversitySuwonRepublic of Korea
  3. 3.Department of Mathematics and Research Institute of Natural SciencesSookmyung Women’s UniversitySeoulRepublic of Korea

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