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Consumption and Portfolio Rules for Time-Inconsistent Investors

  • Jesus Marin-Solano
  • Jorge Navas

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.

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File URL: http://arxiv.org/pdf/0901.2484
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Paper provided by arXiv.org in its series Papers with number 0901.2484.

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Date of creation: Jan 2009
Date of revision: Mar 2009
Handle: RePEc:arx:papers:0901.2484
Contact details of provider: Web page: http://arxiv.org/

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  1. 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.
  2. Christopher Harris & David Laibson, 2001. "Instantaneous Gratification," NajEcon Working Paper Reviews 625018000000000267, www.najecon.org.
  3. Jesus Marin Solano & Jorge Navas Rodenes, 2007. "Non-constant discounting in finite horizon: The free terminal time case," Working Papers in Economics 183, Universitat de Barcelona. Espai de Recerca en Economia.
  4. 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 247-57, August.
  5. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
  6. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
  7. Laibson, David I., 1997. "Golden Eggs and Hyperbolic Discounting," Scholarly Articles 4481499, Harvard University Department of Economics.
  8. 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.
  9. Steven R. Grenadier & Neng Wang, 2006. "Investment Under Uncertainty and Time-Inconsistent Preferences," NBER Working Papers 12042, National Bureau of Economic Research, Inc.
  10. Loewenstein, George & Prelec, Drazen, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, MIT Press, vol. 107(2), pages 573-97, May.
  11. Robert J. Barro, 1999. "Ramsey Meets Laibson In The Neoclassical Growth Model," The Quarterly Journal of Economics, MIT Press, vol. 114(4), pages 1125-1152, November.
  12. 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.
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