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Consumption and Portfolio Rules for Time-Inconsistent Investors

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  • Jesus Marin-Solano
  • Jorge Navas

Abstract

This paper extends the classical consumption and portfolio rules model in continuous time (Merton 1969, 1971) 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 potential cases) 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

  • Jesus Marin-Solano & Jorge Navas, 2009. "Consumption and Portfolio Rules for Time-Inconsistent Investors," Papers 0901.2484, arXiv.org, revised Mar 2009.
  • Handle: RePEc:arx:papers:0901.2484
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    References listed on IDEAS

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    Cited by:

    1. Zeng, Yan & Li, Zhongfei & Lai, Yongzeng, 2013. "Time-consistent investment and reinsurance strategies for mean–variance insurers with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 498-507.
    2. Wang, Tianxiao & Yong, Jiongmin, 2015. "Comparison theorems for some backward stochastic Volterra integral equations," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1756-1798.
    3. Pirvu, Traian A. & Zhang, Huayue, 2014. "Investment–consumption with regime-switching discount rates," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 142-150.
    4. Marín-Solano, Jesús & Navas, Jorge & Roch, Oriol, 2013. "Non-constant discounting and consumption, portfolio and life insurance rules," Economics Letters, Elsevier, vol. 119(2), pages 186-190.
    5. Chen, An & Vellekoop, Michel, 2017. "Optimal investment and consumption when allowing terminal debt," European Journal of Operational Research, Elsevier, vol. 258(1), pages 385-397.
    6. de-Paz, Albert & Marín-Solano, Jesús & Navas, Jorge, 2013. "A consumption–investment problem with heterogeneous discounting," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 221-232.
    7. repec:spr:orspec:v:40:y:2018:i:2:d:10.1007_s00291-017-0502-2 is not listed on IDEAS
    8. Zhao, Qian & Wei, Jiaqin & Wang, Rongming, 2014. "On dividend strategies with non-exponential discounting," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 1-13.
    9. repec:cys:ecocyb:v:50:y:2017:i:2:p:145-164 is not listed on IDEAS
    10. repec:gam:jrisks:v:6:y:2018:i:2:p:43-:d:142704 is not listed on IDEAS
    11. Haruvy, Ernan E. & Li, Tao & Sethi, Suresh P., 2012. "Two-stage pricing for custom-made products," European Journal of Operational Research, Elsevier, vol. 219(2), pages 405-414.
    12. de-Paz, Albert & Marín-Solano, Jesús & Navas, Jorge & Roch, Oriol, 2014. "Consumption, investment and life insurance strategies with heterogeneous discounting," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 66-75.
    13. 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.
    14. repec:eee:insuma:v:74:y:2017:i:c:p:31-45 is not listed on IDEAS
    15. Traian Pirvu & Huayue Zhang, 2013. "Investment and Consumption with Regime-Switching Discount Rates," Papers 1303.1248, arXiv.org.
    16. 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.
    17. Tomas Björk & Mariana Khapko & Agatha Murgoci, 2017. "On time-inconsistent stochastic control in continuous time," Finance and Stochastics, Springer, vol. 21(2), pages 331-360, April.
    18. Schendel, Lorenz S., 2014. "Consumption-investment problems with stochastic mortality risk," SAFE Working Paper Series 43, Research Center SAFE - Sustainable Architecture for Finance in Europe, Goethe University Frankfurt.
    19. 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.
    20. Matsui, Kenji, 2010. "Returns policy, new model introduction, and consumer welfare," International Journal of Production Economics, Elsevier, vol. 124(2), pages 299-309, April.

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