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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
File Function: Latest version
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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. 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.
  2. 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.
  3. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 573-597.
  4. Grenadier, Steven R. & Wang, Neng, 2005. "Investment under Uncertainty and Time-Inconsistent Preferences," Research Papers 1899, Stanford University, Graduate School of Business.
  5. Karp, Larry, 2004. "Non-constant discounting in continuous time," CUDARE Working Paper Series 0969, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.
  6. Chang,Fwu-Ranq, 2004. "Stochastic Optimization in Continuous Time," Cambridge Books, Cambridge University Press, number 9780521834063, June.
  7. Christopher Harris & David Laibson, 2006. "Instantaneous Gratification," Levine's Bibliography 321307000000000635, UCLA Department of Economics.
  8. R. A. Pollak, 1968. "Consistent Planning," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 201-208.
  9. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 185-199.
  10. Robert J. Barro, 1999. "Ramsey Meets Laibson in the Neoclassical Growth Model," The Quarterly Journal of Economics, Oxford University Press, vol. 114(4), pages 1125-1152.
  11. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
  12. 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.
  13. 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.
  14. 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.
  15. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
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