IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v33y2009i3p666-675.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(08)00153-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. R. A. Pollak, 1968. "Consistent Planning," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 201-208.
    2. Karp, Larry, 2007. "Non-constant discounting in continuous time," Journal of Economic Theory, Elsevier, vol. 132(1), pages 557-568, January.
    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, 2008. "Time perspective and climate change policy," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt04k4b21g, Department of Agricultural & Resource Economics, UC Berkeley.
    5. 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.
    6. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 573-597.
    7. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    8. Robert J. Barro, 1999. "Ramsey Meets Laibson in the Neoclassical Growth Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(4), pages 1125-1152.
    9. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    10. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 185-199.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Peng, Ling & Kloeden, Peter E., 2021. "Time-consistent portfolio optimization," European Journal of Operational Research, Elsevier, vol. 288(1), pages 183-193.
    2. Nian Yang & Jun Yang & Yu Chen, 2018. "Contracting in a Continuous-Time Model with Three-Sided Moral Hazard and Cost Synergies," Graz Economics Papers 2018-06, University of Graz, Department of Economics.
    3. Josa-Fombellida, Ricardo & Navas, Jorge, 2020. "Time consistent pension funding in a defined benefit pension plan with non-constant discounting," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 142-153.
    4. Francisco Cabo & Guiomar Martín-Herrán & María Pilar Martínez-García, 2020. "Non-constant Discounting, Social Welfare and Endogenous Growth with Pollution Externalities," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 76(2), pages 369-403, July.
    5. Huiling Wu & Chengguo Weng & Yan Zeng, 2018. "Equilibrium consumption and portfolio decisions with stochastic discount rate and time-varying utility functions," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(2), pages 541-582, March.
    6. Raouf Boucekkine & Blanca Martínez & J. Ramon Ruiz-Tamarit, 2018. "Optimal Population Growth as an Endogenous Discounting Problem: The Ramsey Case," Lecture Notes in Economics and Mathematical Systems, in: Gustav Feichtinger & Raimund M. Kovacevic & Gernot Tragler (ed.), Control Systems and Mathematical Methods in Economics, pages 321-347, Springer.
    7. 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.
    8. 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.
    9. Carles Mañó-Cabello & Jesús Marín-Solano & Jorge Navas, 2021. "A Resource Extraction Model with Technology Adoption under Time Inconsistent Preferences," Mathematics, MDPI, vol. 9(18), pages 1-24, September.
    10. 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," LIDAM Discussion Papers IRES 2017020, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    11. Feigenbaum, James & Raei, Sepideh, 2023. "Lifecycle consumption and welfare with nonexponential discounting in continuous time," Journal of Mathematical Economics, Elsevier, vol. 107(C).
    12. Schendel, Lorenz S., 2014. "Consumption-investment problems with stochastic mortality risk," SAFE Working Paper Series 43, Leibniz Institute for Financial Research SAFE.
    13. 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.
    14. Escribá-Pérez, F.J. & Murgui-García, M.J. & Ruiz-Tamarit, J.R., 2018. "Economic and statistical measurement of physical capital: From theory to practice," Economic Modelling, Elsevier, vol. 75(C), pages 246-255.
    15. 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.
    16. 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.
    17. Cabo, Francisco & Martín-Herrán, Guiomar & Martínez-García, María Pilar, 2020. "Present bias and the inefficiency of the centralized economy: The role of the elasticity of intertemporal substitution," Economic Modelling, Elsevier, vol. 93(C), pages 702-716.
    18. 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.
    19. Feigenbaum, James, 2016. "Equivalent representations of non-exponential discounting models," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 58-71.
    20. Chen Shou & Xiang Shengpeng & He Hongbo, 2019. "Do Time Preferences Matter in Intertemporal Consumption and Portfolio Decisions?," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 19(2), pages 1-13, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Iverson, Terrence, 2012. "Optimal Carbon Taxes with Non-Constant Time Preference," MPRA Paper 43264, University Library of Munich, Germany.
    2. 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.
    3. Terrence Iverson & Scott Denning & Sammy Zahran, 2015. "When the long run matters," Climatic Change, Springer, vol. 129(1), pages 57-72, March.
    4. Francisco Cabo & Guiomar Martín-Herrán & María Pilar Martínez-García, 2020. "Non-constant Discounting, Social Welfare and Endogenous Growth with Pollution Externalities," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 76(2), pages 369-403, July.
    5. Drouhin, Nicolas, 2020. "Non-stationary additive utility and time consistency," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 1-14.
    6. 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.
    7. Hammond, Peter J & Zank, Horst, 2013. "Rationality and Dynamic Consistency under Risk and Uncertainty," The Warwick Economics Research Paper Series (TWERPS) 1033, University of Warwick, Department of Economics.
    8. Kang, Minwook & Kim, Eungsik, 2023. "A government policy with time-inconsistent consumers," Journal of Economic Behavior & Organization, Elsevier, vol. 214(C), pages 44-67.
    9. Terrence Iverson & Larry Karp, 2021. "Carbon Taxes and Climate Commitment with Non-constant Time Preference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(2), pages 764-799.
    10. 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.
    11. Yu-Jui Huang & Adrien Nguyen-Huu, 2018. "Time-consistent stopping under decreasing impatience," Finance and Stochastics, Springer, vol. 22(1), pages 69-95, January.
    12. Maria Arvaniti & Chandra K. Krishnamurthy & Anne-Sophie Crépin, 2019. "Time-consistent resource management with regime shifts," CER-ETH Economics working paper series 19/329, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    13. O'Donoghue, Ted & Rabin, Matthew, 2008. "Procrastination on long-term projects," Journal of Economic Behavior & Organization, Elsevier, vol. 66(2), pages 161-175, May.
    14. Philip Streich & Jack S. Levy, 2007. "Time Horizons, Discounting, and Intertemporal Choice," Journal of Conflict Resolution, Peace Science Society (International), vol. 51(2), pages 199-226, April.
    15. Faralla, Valeria & Novarese, Marco & Ardizzone, Antonella, 2017. "Framing Effects in Intertemporal Choice: A Nudge Experiment," MPRA Paper 82086, University Library of Munich, Germany.
    16. Dorian Jullien, 2018. "Under Risk, Over Time, Regarding Other People: Language and Rationality within Three Dimensions," Research in the History of Economic Thought and Methodology, in: Including a Symposium on Latin American Monetary Thought: Two Centuries in Search of Originality, volume 36, pages 119-155, Emerald Group Publishing Limited.
    17. Tyson, Christopher J., 2008. "Management of a capital stock by Strotz's naive planner," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2214-2239, July.
    18. 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.
    19. Bernergård, Axel, 2011. "Folk Theorems for Present-Biased Players," SSE/EFI Working Paper Series in Economics and Finance 736, Stockholm School of Economics.
    20. Takeo Hori & Koichi Futagami, 2019. "A Non‐unitary Discount Rate Model," Economica, London School of Economics and Political Science, vol. 86(341), pages 139-165, January.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:33:y:2009:i:3:p:666-675. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.