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

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  • Jesus Marin Solano
  • Jorge Navas Rodenes

    (Universitat de Barcelona)

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. A simple example is used in order to illustrate the applicability of this HJB equation, by suggesting a method for constructing the subgame perfect equilibrium solution to the problem. Conditions for the observational equivalence with an associated problem with constant discounting are analyzed. Special attention is paid to the case of free terminal time. Strotzs model (an eating cake problem of a nonrenewable resource with non-constant discounting) is revisited.

Suggested Citation

  • 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.
    • Handle: RePEc:bar:bedcje:2007183
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    Cited by:

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    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.

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    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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