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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
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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. 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.
    3. Richard, Scott F., 1975. "Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model," Journal of Financial Economics, Elsevier, vol. 2(2), pages 187-203, June.
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    8. 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.
    9. Karp, Larry, 2007. "Non-constant discounting in continuous time," Journal of Economic Theory, Elsevier, vol. 132(1), pages 557-568, January.
    10. 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.
    11. repec:dau:papers:123456789/11473 is not listed on IDEAS
    12. 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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    17. Holger Kraft, 2003. "Elasticity approach to portfolio optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(1), pages 159-182, September.
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    Cited by:

    1. Peng, Ling & Kloeden, Peter E., 2021. "Time-consistent portfolio optimization," European Journal of Operational Research, Elsevier, vol. 288(1), pages 183-193.
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    3. Ekaterina Gromova & Anastasiia Zaremba & Shimai Su, 2021. "Time-Consistency of an Imputation in a Cooperative Hybrid Differential Game," Mathematics, MDPI, vol. 9(15), pages 1-14, August.
    4. Zhang, Jinhui & Purcal, Sachi & Wei, Jiaqin, 2021. "Optimal life insurance and annuity demand under hyperbolic discounting when bequests are luxury goods," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 80-90.

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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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