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Time-consistency of optimal investment under smooth ambiguity

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  • Balter, Anne G.
  • Mahayni, Antje
  • Schweizer, Nikolaus

Abstract

We study portfolio choice in a Black–Scholes world under drift uncertainty. Preferences towards risk and ambiguity are modeled using the smooth ambiguity approach under a double power utility assumption and a normal distribution assumption on the unknown drift. Optimal investment in this setting is time-inconsistent. Utility is maximized by a time-inconsistent pre-commitment strategy resembling the classical Merton solution. In contrast, the optimal dynamically consistent investment strategy accounts for variations in the perceived severity of drift uncertainty, increasing the riskiness of the strategy gradually over time. We provide a detailed comparative analysis of the mechanics and interplay of ambiguity, myopia and optimal decisions in this setting. We show that an investor who pre-commits will regret that decision from some time point onwards, wishing that she had followed the dynamically consistent strategy.

Suggested Citation

  • Balter, Anne G. & Mahayni, Antje & Schweizer, Nikolaus, 2021. "Time-consistency of optimal investment under smooth ambiguity," European Journal of Operational Research, Elsevier, vol. 293(2), pages 643-657.
    • Handle: RePEc:eee:ejores:v:293:y:2021:i:2:p:643-657
    DOI: 10.1016/j.ejor.2020.12.046
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    1. Guan, Guohui & Li, Bin, 2022. "Equilibrium investment and reinsurance strategies under smooth ambiguity with a general second-order distribution," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    2. Guo, Sini & Gu, Jia-Wen & Ching, Wai-Ki, 2021. "Adaptive online portfolio selection with transaction costs," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1074-1086.
    3. Julian Holzermann, 2023. "Optimal Investment with Stochastic Interest Rates and Ambiguity," Papers 2306.13343, arXiv.org, revised Oct 2023.
    4. Wang, Tao & Chen, Zhiping, 2024. "Optimal portfolio and insurance strategy with biometric risks, habit formation and smooth ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 118(C), pages 195-222.
    5. Balter, Anne G. & Schweizer, Nikolaus, 2024. "Robust decisions for heterogeneous agents via certainty equivalents," European Journal of Operational Research, Elsevier, vol. 317(1), pages 171-184.
    6. Francesca Biagini & Andrea Mazzon & Katharina Oberpriller, 2023. "Multi-dimensional fractional Brownian motion in the G-setting," Papers 2312.12139, arXiv.org, revised Nov 2024.
    7. Felix Fie{ss}inger & Mitja Stadje, 2023. "Time-Consistent Asset Allocation for Risk Measures in a L\'evy Market," Papers 2305.09471, arXiv.org, revised Oct 2024.
    8. Anne G. Balter & Nikolaus Schweizer, 2021. "Robust Decisions for Heterogeneous Agents via Certainty Equivalents," Papers 2106.13059, arXiv.org.
    9. Fereydooni, Ali & Barak, Sasan & Asaad Sajadi, Seyed Mehrzad, 2024. "A novel online portfolio selection approach based on pattern matching and ESG factors," Omega, Elsevier, vol. 123(C).
    10. Len Patrick Dominic M. Garces & Yang Shen, 2024. "Robust optimal investment and consumption strategies with portfolio constraints and stochastic environment," Papers 2407.02831, arXiv.org.
    11. Nicole Bauerle & Antje Mahayni, 2023. "Optimal investment in ambiguous financial markets with learning," Papers 2303.08521, arXiv.org, revised Feb 2024.
    12. Keffert, Henk, 2024. "Robo-advising: Optimal investment with mismeasured and unstable risk preferences," European Journal of Operational Research, Elsevier, vol. 315(1), pages 378-392.
    13. Guohui Guan & Zongxia Liang & Yilun Song, 2022. "The continuous-time pre-commitment KMM problem in incomplete markets," Papers 2210.13833, arXiv.org, revised Feb 2023.
    14. Bäuerle, Nicole & Mahayni, Antje, 2024. "Optimal investment in ambiguous financial markets with learning," European Journal of Operational Research, Elsevier, vol. 315(1), pages 393-410.

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