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Non-constant discounting in finite horizon: The free terminal time case

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  • Marín-Solano, Jesús
  • Navas, Jorge

Abstract

This paper derives the HJB (Hamilton-Jacobi-Bellman) equation for sophisticated agents in a finite horizon dynamic optimization problem with non-constant discounting in a continuous setting, by using a dynamic programming approach. Special attention is paid to the case of free terminal time. Strotz's model (a cake-eating problem of a non-renewable resource with non-constant discounting) is revisited. A consumption-saving model is used to illustrate the results in the free terminal time case.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:dyncon:v:33:y:2009:i:3:p:666-675
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    References listed on IDEAS

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    1. R. A. Pollak, 1968. "Consistent Planning," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 201-208.
    2. Karp, Larry, 2007. "Non-constant discounting in continuous time," Journal of Economic Theory, Elsevier, pages 557-568.
    3. Karp, Larry, 2005. "Global warming and hyperbolic discounting," Journal of Public Economics, Elsevier, vol. 89(2-3), pages 261-282, February.
    4. Karp, Larry & Tsur, Yacov, 2011. "Time perspective and climate change policy," Journal of Environmental Economics and Management, Elsevier, pages 1-14.
    5. 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.
    6. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    7. 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.
    8. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
    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. Karp, Larry & Tsur, Yacov, 2011. "Time perspective and climate change policy," Journal of Environmental Economics and Management, Elsevier, vol. 62(1), pages 1-14, July.
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    Citations

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    Cited by:

    1. Raouf Boucekkine & Blanca Martínez & José Ramón Ruiz-Tamarit, 2017. "Optimal Population Growth as an Endogenous Discounting Problem: The Ramsey Case," AMSE Working Papers 1731, Aix-Marseille School of Economics, Marseille, France.
    2. Caputo, Michael R., 2013. "The intrinsic comparative dynamics of infinite horizon optimal control problems with a time-varying discount rate and time-distance discounting," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 810-820.
    3. Marín-Solano, Jesús & Navas, Jorge, 2010. "Consumption and portfolio rules for time-inconsistent investors," European Journal of Operational Research, Elsevier, vol. 201(3), pages 860-872, March.
    4. F. J. Escribá-Pérez & M. J. Murgui-García & J. R. Ruiz-Tamarit, 2017. "Economic and Statistical Measurement of Physical Capital with an Application to the Spanish Economy," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2017020, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    5. 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.
    6. Cabo, Francisco & Martín-Herrán, Guiomar & Martínez-García, María Pilar, 2016. "Unbounded growth in the Neoclassical growth model with non-constant discounting," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 93-104.
    7. 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.
    8. Zhao, Qian & Shen, Yang & Wei, Jiaqin, 2014. "Consumption–investment strategies with non-exponential discounting and logarithmic utility," European Journal of Operational Research, Elsevier, vol. 238(3), pages 824-835.
    9. Albert de-Paz & Jesus Marin-Solano & Jorge Navas, 2011. "Time Consistent Pareto Solutions in Common Access Resource Games with Asymmetric Players," Working Papers in Economics 253, Universitat de Barcelona. Espai de Recerca en Economia.
    10. Feigenbaum, James, 2016. "Equivalent representations of non-exponential discounting models," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 58-71.

    More about this item

    Keywords

    Non-constant discounting Naive and sophisticated agents Free terminal time;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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