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Heterogeneous discounting in consumption-investment problems. Time consistent solutions

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  • Albert de-Paz
  • Jesus Marin-Solano
  • Jorge Navas

    (Universitat de Barcelona)

Abstract

In this paper we analyze a stochastic continuous time model in finite horizon in which agents discount the instantaneous utility function and the final function at constant but different instantaneous discount rates of time preference. Within this context we can model problems in which, when the time t approaches to the final time, the valuation of the final function increases compared with previous valuations in a way that cannot be explained by using a unique constant or a variable discount rate. We derive a dynamic programming equation whose solutions are time-consistent Markov equilibria. For this class of time preferences, we study the classical consumption and portfolio rules model (Merton, 1971) for CRRA and CARA utility functions for time- consistent agents, and we compare the different equilibria with the time-inconsistent solutions. The introduction of stochastic terminal time is also discussed.

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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 264.

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Length: 0 pages
Date of creation: 2011
Date of revision:
Handle: RePEc:bar:bedcje:2011264

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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. 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.
  2. 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.
  3. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
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