IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v201y2010i3p860-872.html
   My bibliography  Save this article

Consumption and portfolio rules for time-inconsistent investors

Author

Listed:
  • Marín-Solano, Jesús
  • Navas, Jorge

Abstract

This paper extends the classical consumption and portfolio rules model in continuous time [Merton, R.C., 1969. Lifetime portfolio selection under uncertainty: The continuous time case. Review of Economics and Statistics 51, 247-257, Merton, R.C., 1971. Optimum consumption and portfolio rules in a continuous time model. Journal of Economic Theory 3, 373-413] to the framework of decision-makers with time-inconsistent preferences. The model is solved for different utility functions for both, naive and sophisticated agents, and the results are compared. In order to solve the problem for sophisticated agents, we derive a modified HJB (Hamilton-Jacobi-Bellman) equation. It is illustrated how for CRRA functions within the family of HARA functions (logarithmic and power utilities) the optimal portfolio rule does not depend on the discount rate, but this is not the case for a general utility function, such as the exponential (CARA) utility function.

Suggested Citation

  • Marín-Solano, Jesús & Navas, Jorge, 2010. "Consumption and portfolio rules for time-inconsistent investors," European Journal of Operational Research, Elsevier, vol. 201(3), pages 860-872, March.
    • Handle: RePEc:eee:ejores:v:201:y:2010:i:3:p:860-872
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(09)00254-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. R. A. Pollak, 1968. "Consistent Planning," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 201-208.
    2. Grenadier, Steven R. & Wang, Neng, 2007. "Investment under uncertainty and time-inconsistent preferences," Journal of Financial Economics, Elsevier, vol. 84(1), pages 2-39, April.
    3. Chang,Fwu-Ranq, 2009. "Stochastic Optimization in Continuous Time," Cambridge Books, Cambridge University Press, number 9780521541947, October.
    4. Tomak, Kerem & Keskin, Tayfun, 2008. "Exploring the trade-off between immediate gratification and delayed network externalities in the consumption of information goods," European Journal of Operational Research, Elsevier, vol. 187(3), pages 887-902, June.
    5. Karp, Larry, 2007. "Non-constant discounting in continuous time," Journal of Economic Theory, Elsevier, vol. 132(1), pages 557-568, January.
    6. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    7. Marín-Solano, Jesús & Navas, Jorge, 2009. "Non-constant discounting in finite horizon: The free terminal time case," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 666-675, March.
    8. Ivar Ekeland & Traian A Pirvu, 2008. "On a Non-Standard Stochastic Control Problem," Papers 0806.4026, arXiv.org.
    9. Josa-Fombellida, Ricardo & Rincon-Zapatero, Juan Pablo, 2008. "Mean-variance portfolio and contribution selection in stochastic pension funding," European Journal of Operational Research, Elsevier, vol. 187(1), pages 120-137, May.
    10. 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.
    11. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 573-597.
    12. Christopher Harris & David Laibson, 2013. "Instantaneous Gratification," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(1), pages 205-248.
    13. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    14. Robert J. Barro, 1999. "Ramsey Meets Laibson in the Neoclassical Growth Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(4), pages 1125-1152.
    15. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    16. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 185-199.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhao, Qian & Shen, Yang & Wei, Jiaqin, 2014. "Consumption–investment strategies with non-exponential discounting and logarithmic utility," European Journal of Operational Research, Elsevier, vol. 238(3), pages 824-835.
    2. Drouhin, Nicolas, 2020. "Non-stationary additive utility and time consistency," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 1-14.
    3. Zou, Ziran & Chen, Shou & Wedge, Lei, 2014. "Finite horizon consumption and portfolio decisions with stochastic hyperbolic discounting," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 70-80.
    4. Chen Shou & Xiang Shengpeng & He Hongbo, 2019. "Do Time Preferences Matter in Intertemporal Consumption and Portfolio Decisions?," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 19(2), pages 1-13, June.
    5. Marín-Solano, Jesús & Navas, Jorge, 2009. "Non-constant discounting in finite horizon: The free terminal time case," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 666-675, March.
    6. Chen, Shumin & Zeng, Yan & Hao, Zhifeng, 2017. "Optimal dividend strategies with time-inconsistent preferences and transaction costs in the Cramér–Lundberg model," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 31-45.
    7. Huiling Wu & Chengguo Weng & Yan Zeng, 2018. "Equilibrium consumption and portfolio decisions with stochastic discount rate and time-varying utility functions," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(2), pages 541-582, March.
    8. Liya Liu & Yingjie Niu & Yuanping Wang & Jinqiang Yang, 2020. "Optimal consumption with time-inconsistent preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 785-815, October.
    9. Koo, Ja Eun & Lim, Byung Hwa, 2021. "Consumption and life insurance decisions under hyperbolic discounting and taxation," Economic Modelling, Elsevier, vol. 94(C), pages 288-295.
    10. Yu-Jui Huang & Adrien Nguyen-Huu, 2018. "Time-consistent stopping under decreasing impatience," Finance and Stochastics, Springer, vol. 22(1), pages 69-95, January.
    11. Chen, Shumin & Luo, Dan & Yao, Haixiang, 2024. "Optimal investor life cycle decisions with time-inconsistent preferences," Journal of Banking & Finance, Elsevier, vol. 161(C).
    12. Tyson, Christopher J., 2008. "Management of a capital stock by Strotz's naive planner," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2214-2239, July.
    13. Hammond, Peter J & Zank, Horst, 2013. "Rationality and Dynamic Consistency under Risk and Uncertainty," The Warwick Economics Research Paper Series (TWERPS) 1033, University of Warwick, Department of Economics.
    14. Li, Yuan & Yang, Jinqiang & Zhao, Siqi, 2022. "Present-biased government and sovereign debt dynamics," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    15. Grenadier, Steven R. & Wang, Neng, 2007. "Investment under uncertainty and time-inconsistent preferences," Journal of Financial Economics, Elsevier, vol. 84(1), pages 2-39, April.
    16. Pengyu Wei & Wei Wei, 2024. "Irreversible investment under weighted discounting: effects of decreasing impatience," Papers 2409.01478, arXiv.org.
    17. Tian, Yuan, 2016. "Optimal capital structure and investment decisions under time-inconsistent preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 65(C), pages 83-104.
    18. Takeo Hori & Koichi Futagami, 2019. "A Non‐unitary Discount Rate Model," Economica, London School of Economics and Political Science, vol. 86(341), pages 139-165, January.
    19. Caputo, Michael R., 2013. "The intrinsic comparative dynamics of infinite horizon optimal control problems with a time-varying discount rate and time-distance discounting," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 810-820.
    20. Nicolas Drouhin, 2016. "Non stationary additive utility and time consistency," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01238584, HAL.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:201:y:2010:i:3:p:860-872. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.