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Approximate analytical solutions for consumption/investment problems under recursive utility and finite horizon

Author

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  • Carlos Heitor Campania

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • René Garcia

    (UdeM - Université de Montréal)

Abstract

We study the asset allocation and consumption decisions of an investor with recursive utility and a finite investment horizon. We provide an approximate analytical solution under a stochastic investment opportunity set. The solution becomes exact when the elasticity of intertemporal substitution is equal to one or under a constant opportunity set. We show that this elasticity impacts both consumption and portfolio strategies, indicating the importance of disentangling intertemporal substitution from risk aversion. The investor's horizon also plays a crucial role in optimal policies and the usual infinite horizon framework is inappropriate for investors having short- or medium-term horizons. Moreover, the infinite horizon problem reveals the existence of conditions on the preference parameters for our solution to hold, raising the question of whether another solution may exist or not. On its turn, the absence of a bequest motive in the finite horizon problem imposes another condition on risk parameters.

Suggested Citation

  • Carlos Heitor Campania & René Garcia, 2019. "Approximate analytical solutions for consumption/investment problems under recursive utility and finite horizon," Post-Print hal-02894663, HAL.
    • Handle: RePEc:hal:journl:hal-02894663
    DOI: 10.1016/j.najef.2019.03.005
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    References listed on IDEAS

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    Cited by:

    1. Goncalo dos Reis & Vadim Platonov, 2020. "Forward utility and market adjustments in relative investment-consumption games of many players," Papers 2012.01235, arXiv.org, revised Mar 2022.
    2. Kraft, Holger & Munk, Claus & Weiss, Farina, 2022. "Bequest motives in consumption-portfolio decisions with recursive utility," Journal of Banking & Finance, Elsevier, vol. 138(C).
    3. Marcelo Lewin & Carlos Heitor Campani, 2023. "Constrained portfolio strategies in a regime-switching economy," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 37(1), pages 27-59, March.
    4. Marine Carrasco & N'Golo Koné, 2023. "Test for Trading Costs Effect in a Portfolio Selection Problem with Recursive Utility," CIRANO Working Papers 2023s-03, CIRANO.

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    More about this item

    Keywords

    Intertemporal hedging; Finite horizon; Stochastic differential utility; Exact analytical solution; Approximate analytical solution;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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