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A consumption–investment problem with heterogeneous discounting


  • de-Paz, Albert
  • Marín-Solano, Jesús
  • Navas, Jorge


We analyze a stochastic continuous time model in finite horizon in which the agent discounts the instantaneous utility function and the final function at constant but different discount rates of time preference. Within this framework 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. We study a consumption and portfolio rules problem for CRRA and CARA utility functions for time-consistent agents, and we compare the different equilibria with the time-inconsistent solutions. The introduction of random terminal time is also discussed. Differences with both the mathematical treatment and agent’s behavior in the case of hyperbolic discounting are stressed.

Suggested Citation

  • de-Paz, Albert & Marín-Solano, Jesús & Navas, Jorge, 2013. "A consumption–investment problem with heterogeneous discounting," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 221-232.
  • Handle: RePEc:eee:matsoc:v:66:y:2013:i:3:p:221-232 DOI: 10.1016/j.mathsocsci.2013.05.001

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    References listed on IDEAS

    1. Karp, Larry, 2007. "Non-constant discounting in continuous time," Journal of Economic Theory, Elsevier, vol. 132(1), pages 557-568, January.
    2. Martin Browning & Thomas F. Crossley, 2001. "The Life-Cycle Model of Consumption and Saving," Journal of Economic Perspectives, American Economic Association, vol. 15(3), pages 3-22, Summer.
    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. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 185-199.
    5. 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.
    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. Serdar Sayman & Ayse Öncüler, 2009. "An Investigation of Time Inconsistency," Management Science, INFORMS, vol. 55(3), pages 470-482, March.
    8. Bleichrodt, Han & Rohde, Kirsten I.M. & Wakker, Peter P., 2009. "Non-hyperbolic time inconsistency," Games and Economic Behavior, Elsevier, vol. 66(1), pages 27-38, May.
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    Cited by:

    1. de-Paz, Albert & Marín-Solano, Jesús & Navas, Jorge & Roch, Oriol, 2014. "Consumption, investment and life insurance strategies with heterogeneous discounting," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 66-75.

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