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Periodic portfolio selection with quasi-hyperbolic discounting

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  • Yushi Hamaguchi
  • Alex S. L. Tse

Abstract

We introduce an infinite-horizon, continuous-time portfolio selection problem faced by an agent with periodic S-shaped preference and present bias. The inclusion of a quasi-hyperbolic discount function leads to time-inconsistency and we characterize the optimal portfolio for a pre-committing, naive and sophisticated agent respectively. In the more theoretically challenging problem with a sophisticated agent, the time-consistent planning strategy can be formulated as an equilibrium to a static mean field game. Interestingly, present bias and naivety do not necessarily result in less desirable risk taking behaviors, while agent's sophistication may lead to excessive leverage (underinvestement) in the bad (good) states of the world.

Suggested Citation

  • Yushi Hamaguchi & Alex S. L. Tse, 2024. "Periodic portfolio selection with quasi-hyperbolic discounting," Papers 2410.18240, arXiv.org.
    • Handle: RePEc:arx:papers:2410.18240
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    References listed on IDEAS

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    1. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2012. "Time-Inconsistent Stochastic Linear--Quadratic Control," Post-Print hal-00691816, HAL.
    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. Arjan B. Berkelaar & Roy Kouwenberg & Thierry Post, 2004. "Optimal Portfolio Choice under Loss Aversion," The Review of Economics and Statistics, MIT Press, vol. 86(4), pages 973-987, November.
    4. 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.
    5. Stephan Meier & Charles Sprenger, 2010. "Present-Biased Preferences and Credit Card Borrowing," American Economic Journal: Applied Economics, American Economic Association, vol. 2(1), pages 193-210, January.
    6. Laibson, David, 1998. "Life-cycle consumption and hyperbolic discount functions," European Economic Review, Elsevier, vol. 42(3-5), pages 861-871, May.
    7. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    8. repec:dau:papers:123456789/11473 is not listed on IDEAS
    9. Harris, Christopher & Laibson, David, 2001. "Dynamic Choices of Hyperbolic Consumers," Econometrica, Econometric Society, vol. 69(4), pages 935-957, July.
    10. Diamond, Peter & Koszegi, Botond, 2003. "Quasi-hyperbolic discounting and retirement," Journal of Public Economics, Elsevier, vol. 87(9-10), pages 1839-1872, September.
    11. Ted O'Donoghue & Matthew Rabin, 2015. "Present Bias: Lessons Learned and to Be Learned," American Economic Review, American Economic Association, vol. 105(5), pages 273-279, May.
    12. Anna Jaśkiewicz & Andrzej S. Nowak, 2021. "Markov decision processes with quasi-hyperbolic discounting," Finance and Stochastics, Springer, vol. 25(2), pages 189-229, April.
    13. 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.
    14. 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.
    15. Oster Sharon M. & Scott Morton Fiona M., 2005. "Behavioral Biases Meet the Market: The Case of Magazine Subscription Prices," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 5(1), pages 1-32, March.
    16. Love, David & Phelan, Gregory, 2015. "Hyperbolic discounting and life-cycle portfolio choice," Journal of Pension Economics and Finance, Cambridge University Press, vol. 14(4), pages 492-524, October.
    17. Akerlof, George A, 1991. "Procrastination and Obedience," American Economic Review, American Economic Association, vol. 81(2), pages 1-19, May.
    18. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    19. Paul Calcott & Vladimir Petkov, 2022. "Excessive consumption and present bias," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(1), pages 113-134, July.
    20. Liu, Bo & Lu, Lei & Mu, Congming & Yang, Jinqiang, 2016. "Time-inconsistent preferences, investment and asset pricing," Economics Letters, Elsevier, vol. 148(C), pages 48-52.
    21. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2017. "Time-Inconsistent Stochastic Linear--Quadratic Control: Characterization and Uniqueness of Equilibrium," Post-Print hal-01139343, HAL.
    22. 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.
    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. Yushi Hamaguchi, 2019. "Time-inconsistent consumption-investment problems in incomplete markets under general discount functions," Papers 1912.01281, arXiv.org, revised Mar 2021.
    25. 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.
    26. 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.
    27. Shigeta, Yuki, 2022. "Quasi-hyperbolic discounting under recursive utility and consumption–investment decisions," Journal of Economic Theory, Elsevier, vol. 204(C).
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