Skip to main content
SpringerLink
Log in

Optimal consumption-leisure, portfolio and retirement selection based on α-maxmin expected CES utility with ambiguity

  • Published:
Applied Mathematics-A Journal of Chinese Universities Aims and scope Submit manuscript

Abstract

This article studies optimal consumption-leisure, portfolio and retirement selection of an infinitely lived investor whose preference is formulated by α-maxmin expected CES utility which is to differentiate ambiguity and ambiguity attitude. Adopting the recursive multiplepriors utility and the technique of backward stochastic differential equations (BSDEs), we transform the α-maxmin expected CES utility into a classical expected CES utility under a new probability measure related to the degree of an investor’s uncertainty. Our model investigates the optimal consumption-leisure-work selection, the optimal portfolio selection, and the optimal stopping problem. In this model, the investor is able to adjust her supply of labor flexibly above a certain minimum work-hour along with a retirement option. The problem can be analytically solved by using a variational inequality. And the optimal retirement time is given as the first time when her wealth exceeds a certain critical level. The optimal consumption-leisure and portfolio strategies before and after retirement are provided in closed forms. Finally, the distinctions of optimal consumption-leisure, portfolio and critical wealth level under ambiguity from those with no vagueness are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S Basak. On the fluctuations in consumption and market returns in the presence of labor and human capital: An equilibrium analysis, J Econom Dynam Control, 1999, 23: 1029–1064.

    Article  MATH  Google Scholar 

  2. Z Bodie, J B Detemple, S Otruba, S Walter. Optimal consumption portfolio choices and retirement planning, J Econom Dynam Control, 2004, 28: 1115–1148.

    Article  MathSciNet  Google Scholar 

  3. Z Bodie, R C Merton, W F Samuelson. Labor supply flexibility and portfolio choice in a life cycle model, J Econom Dynam Control, 1992, 16: 427–449.

    Article  Google Scholar 

  4. A Chateauneuf, F Maccheroni, M Marinacci, J M Tallon. Monotone continuous multiple priors, Econom Theory, 2005, 26: 973–982.

    Article  MathSciNet  MATH  Google Scholar 

  5. Z Chen, L G Epstein. Ambiguity, risk, and asset returns in continuous time, Econometrica, 2002, 70: 1403–1443.

    Article  MathSciNet  MATH  Google Scholar 

  6. K J Choi, G Shim. Disutility, optimal retirement, and portfolio selection, Math Finance, 2006, 16: 443–467.

    Article  MathSciNet  MATH  Google Scholar 

  7. K J Choi, G Shim, Y H Shin. Optimal portfolio consumption-leisure and retirement choice problem with CES utility, Math Finance, 2008, 18: 445–472.

    Article  MathSciNet  MATH  Google Scholar 

  8. M S Eichenbaum, L PHansen, K J Singelton. A time series analysis of representative agent models of consumption and leisure choice under uncertainty, Q J Econ, 1988, 103: 51–78.

    Article  Google Scholar 

  9. D Ellsberg. Risk, ambiguity, and the Savage axioms, Q J Econ, 1961, 75: 643–699.

    Article  Google Scholar 

  10. N El Karoui, S Peng, M C Quenez. Backward stochastic differential equations in finance, Math Finance, 1997, 7: 1–71.

    Article  MathSciNet  MATH  Google Scholar 

  11. E Farhi, S Panageas. Saving and investing for early retirement: A theoretical analysis, J Financ Econ, 2007, 83: 87–121.

    Article  Google Scholar 

  12. W Y Fei. Optimal consumption and portfolio choice with ambiguity and anticipation, Inform Sci, 2007, 117: 5178–5190.

    Article  Google Scholar 

  13. W Y Fei. Optimal portfolio choice based on α-MEU under ambiguity, Stochastic Models, 2009, 25: 455–482.

    Article  MathSciNet  MATH  Google Scholar 

  14. W Y Fei, R Q Wu. Anticipative portfolio optimization under constraints and a higher interest rate for borrowing, Stochastic Anal Appl, 2002, 20: 311–345.

    Article  MathSciNet  MATH  Google Scholar 

  15. W Y Fei, R Q Wu. Optimization of utility for ‘large investor’ with anticipation, Stochastic Anal Appl, 2003, 21: 329–358.

    Article  MathSciNet  MATH  Google Scholar 

  16. P Ghirardato, F Maccheroni, M Marinacci. Differentiating ambiguity and ambiguity attitude, J Econom Theory, 2004, 118: 133–173.

    Article  MathSciNet  MATH  Google Scholar 

  17. I Gilboa, D Schmeidler. Maxmin expected utility with a non-unique prior, J Math Econom, 1989, 18: 141–153.

    Article  MathSciNet  MATH  Google Scholar 

  18. M P Jeanblanc, P Lakner, A Kadam. Optimal bankruptcy and consumption/investment policies on an infinite horizon with a continuous debt repayment until bankruptcy, Math Oper Res, 2004, 29: 649–671.

    Article  MathSciNet  MATH  Google Scholar 

  19. H Q Jin, X Y Zhou. Behavioral portfolio selection in continuous time, Math Finance, 2008, 18: 385–426.

    Article  MathSciNet  MATH  Google Scholar 

  20. D Kahneman, A Tversky. Choices, Values and Frames, Cambridge University Press, Cambridge, 2000.

    Google Scholar 

  21. I Karatzas, J P Lehoczky, S P Sethi, S E Shreve. Explicit solution of a general consumption/ investment problem, Math Oper Res, 1986, 11: 261–294.

    Article  MathSciNet  Google Scholar 

  22. I Karatzas, H Wang. Utility maximization with discretionary stopping, SIAM J Control Optim, 2000, 39: 306–329.

    Article  MathSciNet  MATH  Google Scholar 

  23. J Kennan. An econometric analysis of fluctuations in aggregate labor supply and demand, Econometrica, 1988, 56: 317–333.

    Article  Google Scholar 

  24. F H Knight. Risk, Uncertainty and Profit, Houghton Mifflin, Boston, 1921.

    Google Scholar 

  25. N G Mankiw, J J Rotemberg, L H Summers. Intertemporal substitution in macroeconomics, Q J Econ, 1985, 100: 225–251.

    Article  Google Scholar 

  26. R Mehra, E Prescott. The equity premium: A puzzle, J Monetary Econ, 1985, 15: 145–161.

    Article  Google Scholar 

  27. B Øksendal. Stochastic Differential Equation, 6th Ed., Springer-Verlag, Berlin Heidelberg, 2005.

    Google Scholar 

  28. S Peng. Probabilistic interpretation for systems of quasilinear parabolic partial differential equations, Stochatics Stohastics Rep, 1991, 37: 61–74.

    MATH  Google Scholar 

  29. F Riedel. Optimal stopping under ambiguity, Econometrica, 2009, 77: 857–908.

    Article  MathSciNet  MATH  Google Scholar 

  30. D Schmeidler. Subjective probability and expected utility without additivity, Econometrica, 1989, 57: 571–587.

    Article  MathSciNet  MATH  Google Scholar 

  31. J M Yong, X Y Zhou. Stochastic Control: Hamilton Systems and HJB Equations, Springer-Verlag, New York, 1999.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, 241000, China

    Wei-yin Fei

Authors
  1. Wei-yin Fei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wei-yin Fei.

Additional information

Supported by National Natural Science Foundation of China (71171003, 71271003), Programming Fund Project of the Humanities and Social Sciences Research of the Ministry of Education of China (12YJA790041), Anhui Natural Science Foundation (090416225, 1208085MG116), and Anhui Natural Science Foundation of Universities (KJ2010A037, KJ2010B026).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fei, Wy. Optimal consumption-leisure, portfolio and retirement selection based on α-maxmin expected CES utility with ambiguity. Appl. Math. J. Chin. Univ. 27, 435–454 (2012). https://doi.org/10.1007/s11766-012-2749-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11766-012-2749-3

MR Subject Classification

Keywords

Search

Navigation