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Heterogeneous discounting in consumption-investment problems. Time consistent solutions

Author

Listed:
  • 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.

Suggested Citation

  • Albert de-Paz & Jesus Marin-Solano & Jorge Navas, 2011. "Heterogeneous discounting in consumption-investment problems. Time consistent solutions," Working Papers in Economics 264, Universitat de Barcelona. Espai de Recerca en Economia.
    • Handle: RePEc:bar:bedcje:2011264
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    References listed on IDEAS

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    1. Karp, Larry, 2005. "Non-Constant Discounting in Continuous Time," Institute for Research on Labor and Employment, Working Paper Series qt0nn1t22z, Institute of Industrial Relations, UC Berkeley.
    2. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    3. 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.
    4. Karp, L, 2007. "Non-constant discounting in continuous time," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt8d52f6w7, Department of Agricultural & Resource Economics, UC Berkeley.
    5. Karp, Larry, 2007. "Non-constant discounting in continuous time," Journal of Economic Theory, Elsevier, vol. 132(1), pages 557-568, January.
    6. 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.
    7. Paul A. Samuelson, 1937. "A Note on Measurement of Utility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 4(2), pages 155-161.
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    More about this item

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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