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Extremal Behavior of Long-Term Investors with Power Utility

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  • Nicole Bauerle
  • Stefanie Grether

Abstract

We consider a Bayesian financial market with one bond and one stock where the aim is to maximize the expected power utility from terminal wealth. The solution of this problem is known, however there are some conjectures in the literature about the long-term behavior of the optimal strategy. In this paper we prove now that for positive coefficient in the power utility the long-term investor is very optimistic and behaves as if the best drift has been realized. In case the coefficient in the power utility is negative the long-term investor is very pessimistic and behaves as if the worst drift has been realized.

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  • Nicole Bauerle & Stefanie Grether, 2017. "Extremal Behavior of Long-Term Investors with Power Utility," Papers 1703.04423, arXiv.org, revised Jun 2017.
    • Handle: RePEc:arx:papers:1703.04423
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    References listed on IDEAS

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    1. Tomas Björk & Mark Davis & Camilla Landén, 2010. "Optimal investment under partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 371-399, April.
    2. Yihong Xia, 2001. "Learning about Predictability: The Effects of Parameter Uncertainty on Dynamic Asset Allocation," Journal of Finance, American Finance Association, vol. 56(1), pages 205-246, February.
    3. Jakša Cvitanić & Ali Lazrak & Lionel Martellini & Fernando Zapatero, 2006. "Dynamic Portfolio Choice with Parameter Uncertainty and the Economic Value of Analysts' Recommendations," The Review of Financial Studies, Society for Financial Studies, vol. 19(4), pages 1113-1156.
    4. Shen, Yang & Siu, Tak Kuen, 2012. "Asset allocation under stochastic interest rate with regime switching," Economic Modelling, Elsevier, vol. 29(4), pages 1126-1136.
    5. Jörn Sass & Ulrich Haussmann, 2004. "Optimizing the terminal wealth under partial information: The drift process as a continuous time Markov chain," Finance and Stochastics, Springer, vol. 8(4), pages 553-577, November.
    6. 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.
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    Cited by:

    1. Bäuerle Nicole & Chen An, 2019. "Optimal retirement planning under partial information," Statistics & Risk Modeling, De Gruyter, vol. 36(1-4), pages 37-55, December.
    2. 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.
    3. Nicole Bauerle & Antje Mahayni, 2023. "Optimal investment in ambiguous financial markets with learning," Papers 2303.08521, arXiv.org, revised Feb 2024.

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