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Certainty Equivalence And Logarithmic Utilities In Consumption/Investment Problems

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  • Yoichi Kuwana

Abstract

We investigate an optimal consumption/investment decision problem with partially observable drift. Logarithmic utilities are shown to be necessary and sufficient for the certainty equivalence principle to hold. For the sufficiency part of the proof, we allow a general stochastic structure about the unobservable drift. On the other hand, a simple Bayesian structure is assumed for the necessity part in order to utilize the Hamilton‐Jacobi‐Bellman equations.

Suggested Citation

  • Yoichi Kuwana, 1995. "Certainty Equivalence And Logarithmic Utilities In Consumption/Investment Problems," Mathematical Finance, Wiley Blackwell, vol. 5(4), pages 297-309, October.
    • Handle: RePEc:bla:mathfi:v:5:y:1995:i:4:p:297-309
    DOI: 10.1111/j.1467-9965.1995.tb00069.x
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    Cited by:

    1. Dalia Ibrahim & Frédéric Abergel, 2018. "Non-linear filtering and optimal investment under partial information for stochastic volatility models," Post-Print hal-01018869, HAL.
    2. Michele Longo & Alessandra Mainini, 2017. "Welfare effects of information and rationality in portfolio decisions under parameter uncertainty," Papers 1709.04387, arXiv.org.
    3. Honda, Toshiki, 2003. "Optimal portfolio choice for unobservable and regime-switching mean returns," Journal of Economic Dynamics and Control, Elsevier, vol. 28(1), pages 45-78, October.
    4. Zongxia Liang & Qi Ye, 2024. "Optimal information acquisition for eliminating estimation risk," Papers 2405.09339, arXiv.org.
    5. Nikolai Dokuchaev, 2015. "Optimal portfolio with unobservable market parameters and certainty equivalence principle," Papers 1502.02352, arXiv.org.
    6. Sühan Altay & Katia Colaneri & Zehra Eksi, 2021. "Optimal convergence trading with unobservable pricing errors," Annals of Operations Research, Springer, vol. 299(1), pages 133-161, April.
    7. Lioui, Abraham & Eldor, Rafael, 1998. "Optimal spreading when spreading is optimal," Journal of Economic Dynamics and Control, Elsevier, vol. 23(2), pages 277-301, September.
    8. Michele Longo & Alessandra Mainini, 2016. "Learning And Portfolio Decisions For Crra Investors," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-21, May.
    9. Sühan Altay & Katia Colaneri & Zehra Eksi, 2018. "Pairs Trading Under Drift Uncertainty And Risk Penalization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-24, November.
    10. Zhuo Jin, 2015. "Optimal Debt Ratio and Consumption Strategies in Financial Crisis," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 1029-1050, September.
    11. Michele Longo & Alessandra Mainini, 2015. "Learning and Portfolio Decisions for HARA Investors," Papers 1502.02968, arXiv.org.
    12. David Feldman, 2007. "Incomplete information equilibria: Separation theorems and other myths," Annals of Operations Research, Springer, vol. 151(1), pages 119-149, April.
    13. Suhan Altay & Katia Colaneri & Zehra Eksi, 2019. "Optimal Convergence Trading with Unobservable Pricing Errors," Papers 1910.01438, arXiv.org, revised Oct 2019.
    14. Dalia Ibrahim & Frédéric Abergel, 2018. "Non-linear filtering and optimal investment under partial information for stochastic volatility models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(3), pages 311-346, June.

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