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Consumption, investment and life insurance strategies with heterogeneous discounting

Author

Listed:
  • Albert de-Paz
  • Jesus Marin-Solano
  • Jorge Navas
  • Oriol Roch

    (Universitat de Barcelona)

Abstract

In this paper we analyze how the optimal consumption, investment and life insur- ance rules are modified by the introduction of a class of time-inconsistent preferences. In particular, we account for the fact that an agents preferences evolve along the planning horizon according to her increasing concern about the bequest left to her descendants and about her welfare at retirement. To this end, we consider a stochas- tic continuous time model with random terminal time for an agent with a known distribution of lifetime under heterogeneous discounting. In order to obtain the time- consistent solution, we solve a non-standard dynamic programming equation. For the case of CRRA and CARA utility functions we compare the explicit solutions for the time-inconsistent and the time-consistent agent. The results are illustrated numeri- cally.

Suggested Citation

  • Albert de-Paz & Jesus Marin-Solano & Jorge Navas & Oriol Roch, 2012. "Consumption, investment and life insurance strategies with heterogeneous discounting," Working Papers in Economics 277, Universitat de Barcelona. Espai de Recerca en Economia.
  • Handle: RePEc:bar:bedcje:2012277
    as

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    References listed on IDEAS

    as
    1. Karp, Larry, 2007. "Non-constant discounting in continuous time," Journal of Economic Theory, Elsevier, pages 557-568.
    2. 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.
    3. 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.
    4. 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.
    5. repec:spr:compst:v:58:y:2003:i:1:p:159-182 is not listed on IDEAS
    6. Pliska, Stanley R. & Ye, Jinchun, 2007. "Optimal life insurance purchase and consumption/investment under uncertain lifetime," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1307-1319, May.
    7. 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.
    8. Leung, Siu Fai, 1994. "Uncertain Lifetime, the Theory of the Consumer, and the Life Cycle Hypothesis," Econometrica, Econometric Society, vol. 62(5), pages 1233-1239, September.
    9. repec:dau:papers:123456789/11473 is not listed on IDEAS
    10. 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.
    11. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
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    More about this item

    JEL classification:

    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • 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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