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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.

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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

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  1. Christopher Harris & David Laibson, 2001. "Instantaneous Gratification," Levine's Working Paper Archive 625018000000000267, David K. Levine.
  2. 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.
  3. Laibson, David I., 1997. "Golden Eggs and Hyperbolic Discounting," Scholarly Articles 4481499, Harvard University Department of Economics.
  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. Grenadier, Steven R. & Wang, Neng, 2005. "Investment under Uncertainty and Time-Inconsistent Preferences," Research Papers 1899, Stanford University, Graduate School of Business.
  6. 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.
  7. 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.
  8. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
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Cited by:
  1. 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.
  2. Traian Pirvu & Huayue Zhang, 2013. "Investment and Consumption with Regime-Switching Discount Rates," Papers 1303.1248, arXiv.org.
  3. Albert de-Paz & Jesus Marin-Solano & Jorge Navas & Oriol Roch, 2012. "Consumption, investment and life insurance strategies with heterogeneous discounting," Working Papers in Economics 277, Universitat de Barcelona. Espai de Recerca en Economia.
  4. Matsui, Kenji, 2010. "Returns policy, new model introduction, and consumer welfare," International Journal of Production Economics, Elsevier, vol. 124(2), pages 299-309, April.
  5. 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.
  6. 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.
  7. 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.
  8. 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.

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