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Finite horizon consumption and portfolio decisions with stochastic hyperbolic discounting

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  • Zou, Ziran
  • Chen, Shou
  • Wedge, Lei

Abstract

We study finite horizon consumption and portfolio decisions of time-inconsistent individuals by incorporating the stochastic hyperbolic preferences of Harris and Laibson (2013) into the classical model of Merton (1969, 1971) with constant relative risk aversion (CRRA). We obtain closed-form solutions for optimal consumption and portfolio choices for sophisticated individuals with log utility and numerical solutions for those with power utility. Compared to the results of Merton, we find that stochastic hyperbolic discounting increases the consumption rate but has no effect on the share of wealth invested in the risky asset.

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  • 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.
    • Handle: RePEc:eee:mateco:v:52:y:2014:i:c:p:70-80
    DOI: 10.1016/j.jmateco.2014.03.002
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    1. Matthew Rabin & Ted O'Donoghue, 1999. "Doing It Now or Later," American Economic Review, American Economic Association, vol. 89(1), pages 103-124, March.
    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. Gong, Liutang & Smith, William & Zou, Heng-fu, 2007. "Consumption and Risk with hyperbolic discounting," Economics Letters, Elsevier, vol. 96(2), pages 153-160, August.
    4. Ted O'Donoghue & Matthew Rabin, 2001. "Choice and Procrastination," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 116(1), pages 121-160.
    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. Drazen Prelec, 2004. "Decreasing Impatience: A Criterion for Non‐stationary Time Preference and “Hyperbolic” Discounting," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(3), pages 511-532, October.
    7. 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.
    8. Christopher Harris & David Laibson, 2013. "Instantaneous Gratification," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(1), pages 205-248.
    9. 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.
    10. Karp, Larry, 2007. "Non-constant discounting in continuous time," Journal of Economic Theory, Elsevier, vol. 132(1), pages 557-568, January.
    11. 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.
    12. repec:dau:papers:123456789/11473 is not listed on IDEAS
    13. 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.
    14. 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.
    15. Jianjun Miao, 2008. "Option exercise with temptation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(3), pages 473-501, March.
    16. Stefano DellaVigna & Ulrike Malmendier, 2004. "Contract Design and Self-Control: Theory and Evidence," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(2), pages 353-402.
    17. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    18. Faruk Gul & Wolfgang Pesendorfer, 2001. "Temptation and Self-Control," Econometrica, Econometric Society, vol. 69(6), pages 1403-1435, November.
    19. Akerlof, George A, 1991. "Procrastination and Obedience," American Economic Review, American Economic Association, vol. 81(2), pages 1-19, May.
    20. Palacios Huerta, Ignacio & Pérez Kakabadse, Alonso, 2013. "Consumption and portfolio rules whit stochastic hyperbolic discounting," IKERLANAK http://www-fae1-eao1-ehu-, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    21. 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.
    22. 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.
    Full references (including those not matched with items on IDEAS)

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