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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.

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Bibliographic Info

Paper provided by Universitat de Barcelona. Espai de Recerca en Economia in its series Working Papers in Economics with number 183.

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Length: 29 pages
Date of creation: 2007
Date of revision:
Handle: RePEc:bar:bedcje:2007183

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Postal: Espai de Recerca en Economia, Facultat de Ciències Econòmiques. Tinent Coronel Valenzuela, Num 1-11 08034 Barcelona. Spain.
Web page: http://www.ere.ub.es
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  1. Laibson, David I., 1997. "Golden Eggs and Hyperbolic Discounting," Scholarly Articles 4481499, Harvard University Department of Economics.
  2. Karp, Larry, 2004. "Global Warming and Hyperbolic Discounting," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt5zh730nc, Department of Agricultural & Resource Economics, UC Berkeley.
  3. Karp, Larry, 2004. "Non-constant discounting in continuous time," CUDARE Working Paper Series 0969, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.
  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. 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.
  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, MIT Press, vol. 114(4), pages 1125-1152, November.
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Cited by:
  1. 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.
  2. 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.
  3. 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.
  4. 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.

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