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Do Time Preferences Matter in Intertemporal Consumption and Portfolio Decisions?

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  • Chen Shou

    (Business School, Hunan University, Changsha, 410082, China)

  • Xiang Shengpeng

    (Business School, Hunan University, Changsha, 410082, China)

  • He Hongbo

    (Business School, Hunan University, Changsha, 410082, China)

Abstract

We study the intertemporal consumption and portfolio rules in the model with the general hyperbolic absolute risk aversion (HARA) utility. The equivalent approximation approach is employed to obtain the Hamilton-Jacobi-Bellman (HJB) equations, and a remarkable property is shown: portfolio rules are independent of the discount function. Moreover, both the consumption and portfolio rates are non-increasing functions of wealth. Particularly illustrative cases examined in detail are the models with the most adopted discount functions, including exponential discounting and hyperbolic discounting. Explicit solutions for intertemporal decisions are found for these special cases, revealing that individual’s time preferences affect the consumption rules only. Moreover, the time-consistent consumption rate under hyperbolic discounting is larger than its counterpart under exponential discounting.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:bejtec:v:19:y:2019:i:2:p:13:n:4
    DOI: 10.1515/bejte-2017-0122
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    References listed on IDEAS

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    1. Webb, Craig S., 2016. "Continuous quasi-hyperbolic discounting," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 99-106.
    2. Chang,Fwu-Ranq, 2009. "Stochastic Optimization in Continuous Time," Cambridge Books, Cambridge University Press, number 9780521541947, September.
    3. Karp, Larry, 2005. "Non-Constant Discounting in Continuous Time," Institute for Research on Labor and Employment, Working Paper Series qt0nn1t22z, Institute of Industrial Relations, UC Berkeley.
    4. 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.
    5. Thaler, Richard H & Shefrin, H M, 1981. "An Economic Theory of Self-Control," Journal of Political Economy, University of Chicago Press, vol. 89(2), pages 392-406, April.
    6. Giat, Yahel & Subramanian, Ajay, 2013. "Dynamic contracting under imperfect public information and asymmetric beliefs," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2833-2861.
    7. Gong, Liutang & Zhong, Ruquan & Zou, Heng-fu, 2012. "On the concavity of the consumption function with the time varying discount rate," Economics Letters, Elsevier, vol. 117(1), pages 99-101.
    8. 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.
    9. 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.
    10. Zhao, Qian & Wang, Rongming & Wei, Jiaqin, 2016. "Exponential utility maximization for an insurer with time-inconsistent preferences," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 89-104.
    11. Grasselli, Martino, 2003. "A stability result for the HARA class with stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 611-627, December.
    12. 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.
    13. Nicola Pavoni & Hakki Yazici, 2017. "Optimal Life‐cycle Capital Taxation under Self‐control Problems," Economic Journal, Royal Economic Society, vol. 127(602), pages 1188-1216, June.
    14. Chang, Hao & Chang, Kai, 2017. "Optimal consumption–investment strategy under the Vasicek model: HARA utility and Legendre transform," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 215-227.
    15. Karp, L, 2007. "Non-constant discounting in continuous time," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt8d52f6w7, Department of Agricultural & Resource Economics, UC Berkeley.
    16. 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.
    17. Karp, Larry, 2007. "Non-constant discounting in continuous time," Journal of Economic Theory, Elsevier, vol. 132(1), pages 557-568, January.
    18. Park, Hyeon & Feigenbaum, James, 2018. "Bounded rationality, lifecycle consumption, and Social Security," Journal of Economic Behavior & Organization, Elsevier, vol. 146(C), pages 65-105.
    19. Yoram Halevy, 2015. "Time Consistency: Stationarity and Time Invariance," Econometrica, Econometric Society, vol. 83, pages 335-352, January.
    20. 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.
    21. 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.
    22. Pan, Jinrui & Webb, Craig S. & Zank, Horst, 2015. "An extension of quasi-hyperbolic discounting to continuous time," Games and Economic Behavior, Elsevier, vol. 89(C), pages 43-55.
    23. 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.
    24. Stefano DellaVigna & Ulrike Malmendier, 2006. "Paying Not to Go to the Gym," American Economic Review, American Economic Association, vol. 96(3), pages 694-719, June.
    25. Delong, Łukasz & Chen, An, 2016. "Asset allocation, sustainable withdrawal, longevity risk and non-exponential discounting," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 342-352.
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    More about this item

    Keywords

    hyperbolic discounting; time consistency; equivalent approximation approach; HJB equation; consumption and portfolio rules;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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