Consumption and Portfolio Rules for Time-Inconsistent Investors
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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- Christopher Harris & David Laibson, 2013.
The Quarterly Journal of Economics,
Oxford University Press, vol. 128(1), pages 205-248.
- Christopher Harris & David Laibson, 2001. "Instantaneous Gratification," NajEcon Working Paper Reviews 625018000000000267, www.najecon.org.
- Laibson, David I. & Harris, Christopher, 2012. "Instantaneous Gratification," Scholarly Articles 9918802, Harvard University Department of Economics.
- Christopher Harris & David Laibson, 2001. "Instantaneous Gratification," Levine's Working Paper Archive 625018000000000267, David K. Levine.
- Christopher Harris & David Laibson, 2006. "Instantaneous Gratification," Levine's Bibliography 321307000000000635, UCLA Department of Economics.
- R. A. Pollak, 1968. "Consistent Planning," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 201-208.
- Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
- 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.
- Grenadier, Steven R. & Wang, Neng, 2005. "Investment under Uncertainty and Time-Inconsistent Preferences," Research Papers 1899, Stanford University, Graduate School of Business.
- Steven R. Grenadier & Neng Wang, 2006. "Investment Under Uncertainty and Time-Inconsistent Preferences," NBER Working Papers 12042, National Bureau of Economic Research, Inc.
- Chang,Fwu-Ranq, 2009. "Stochastic Optimization in Continuous Time," Cambridge Books, Cambridge University Press, number 9780521541947, May.
- 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.
- Karp, Larry, 2007. "Non-constant discounting in continuous time," Journal of Economic Theory, Elsevier, vol. 132(1), pages 557-568, January.
- Karp, Larry, 2004. "Non-Constant Discounting in Continuous Time," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt7pr05084, Department of Agricultural & Resource Economics, UC Berkeley.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
- 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.
- Ivar Ekeland & Traian A Pirvu, 2008. "On a Non-Standard Stochastic Control Problem," Papers 0806.4026, arXiv.org.
- 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.
- 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.
- 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. Full references (including those not matched with items on IDEAS)
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