IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1402.6313.html
   My bibliography  Save this paper

Expert Opinions and Logarithmic Utility Maximization in a Market with Gaussian Drift

Author

Listed:
  • Abdelali Gabih
  • Hakam Kondakji
  • Jorn Sass
  • Ralf Wunderlich

Abstract

This paper investigates optimal portfolio strategies in a financial market where the drift of the stock returns is driven by an unobserved Gaussian mean reverting process. Information on this process is obtained from observing stock returns and expert opinions. The latter provide at discrete time points an unbiased estimate of the current state of the drift. Nevertheless, the drift can only be observed partially and the best estimate is given by the conditional expectation given the available information, i.e., by the filter. We provide the filter equations in the model with expert opinion and derive in detail properties of the conditional variance. For an investor who maximizes expected logarithmic utility of his portfolio, we derive the optimal strategy explicitly in different settings for the available information. The optimal expected utility, the value function of the control problem, depends on the conditional variance. The bounds and asymptotic results for the conditional variances are used to derive bounds and asymptotic properties for the value functions. The results are illustrated with numerical examples.

Suggested Citation

  • Abdelali Gabih & Hakam Kondakji & Jorn Sass & Ralf Wunderlich, 2014. "Expert Opinions and Logarithmic Utility Maximization in a Market with Gaussian Drift," Papers 1402.6313, arXiv.org.
    • Handle: RePEc:arx:papers:1402.6313
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1402.6313
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rudiger Frey & Abdelali Gabih & Ralf Wunderlich, 2013. "Portfolio Optimization under Partial Information with Expert Opinions: a Dynamic Programming Approach," Papers 1303.2513, arXiv.org, revised Feb 2014.
    2. Lakner, Peter, 1998. "Optimal trading strategy for an investor: the case of partial information," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 77-97, August.
    3. Rüdiger Frey & Abdelali Gabih & Ralf Wunderlich, 2012. "Portfolio Optimization Under Partial Information With Expert Opinions," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.), Finance at Fields, chapter 11, pages 265-282, World Scientific Publishing Co. Pte. Ltd..
    4. Brendle, Simon, 2006. "Portfolio selection under incomplete information," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 701-723, May.
    5. Katrin Schöttle & Ralf Werner & Rudi Zagst, 2010. "Comparison and robustification of Bayes and Black-Litterman models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(3), pages 453-475, June.
    6. 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.
    7. Lakner, Peter, 1995. "Utility maximization with partial information," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 247-273, April.
    8. 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.
    9. Rüdiger Frey & Abdelali Gabih & Ralf Wunderlich, 2012. "Portfolio Optimization Under Partial Information With Expert Opinions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-18.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Katia Colaneri & Stefano Herzel & Marco Nicolosi, 2021. "The value of knowing the market price of risk," Annals of Operations Research, Springer, vol. 299(1), pages 101-131, April.
    2. Jörn Sass & Dorothee Westphal & Ralf Wunderlich, 2017. "Expert Opinions And Logarithmic Utility Maximization For Multivariate Stock Returns With Gaussian Drift," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 1-41, June.
    3. Abdelali Gabih & Hakam Kondakji & Ralf Wunderlich, 2024. "Power utility maximization with expert opinions at fixed arrival times in a market with hidden Gaussian drift," Annals of Operations Research, Springer, vol. 341(2), pages 897-936, October.
    4. Jorn Sass & Dorothee Westphal, 2020. "Robust Utility Maximization in a Multivariate Financial Market with Stochastic Drift," Papers 2009.14559, arXiv.org, revised May 2021.
    5. Mark H.A. Davis & Sébastien Lleo, 2021. "Risk‐sensitive benchmarked asset management with expert forecasts," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1162-1189, October.
    6. Abdelali Gabih & Hakam Kondakji & Ralf Wunderlich, 2018. "Asymptotic Filter Behavior for High-Frequency Expert Opinions in a Market with Gaussian Drift," Papers 1812.03453, arXiv.org, revised Mar 2020.
    7. Kexin Chen & Hoi Ying Wong, 2022. "Duality in optimal consumption--investment problems with alternative data," Papers 2210.08422, arXiv.org, revised Jul 2023.
    8. Christoph Knochenhauer & Alexander Merkel & Yufei Zhang, 2024. "Optimal Investment with Costly Expert Opinions," Papers 2409.11569, arXiv.org.
    9. Abdelali Gabih & Hakam Kondakji & Ralf Wunderlich, 2022. "Well Posedness of Utility Maximization Problems Under Partial Information in a Market with Gaussian Drift," Papers 2205.08614, arXiv.org, revised Jul 2024.
    10. Jorn Sass & Dorothee Westphal & Ralf Wunderlich, 2018. "Diffusion Approximations for Expert Opinions in a Financial Market with Gaussian Drift," Papers 1807.00568, arXiv.org, revised Mar 2020.
    11. Abdelali Gabih & Ralf Wunderlich, 2023. "Portfolio Optimization in a Market with Hidden Gaussian Drift and Randomly Arriving Expert Opinions: Modeling and Theoretical Results," Papers 2308.02049, arXiv.org, revised Jun 2024.
    12. Mark Davis & Sébastien Lleo, 2024. "Jump-diffusion risk-sensitive benchmarked asset management with traditional and alternative data," Annals of Operations Research, Springer, vol. 336(1), pages 661-689, May.
    13. Davis, Mark & Lleo, Sébastien, 2020. "Debiased expert forecasts in continuous-time asset allocation," Journal of Banking & Finance, Elsevier, vol. 113(C).
    14. Sangmin Lee & Andrew Papanicolaou, 2016. "Pairs Trading Of Two Assets With Uncertainty In Co-Integration'S Level Of Mean Reversion," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1-36, December.
    15. Jorn Sass & Dorothee Westphal & Ralf Wunderlich, 2016. "Expert Opinions and Logarithmic Utility Maximization for Multivariate Stock Returns with Gaussian Drift," Papers 1601.08155, arXiv.org, revised Mar 2016.
    16. S'ebastien Lleo & Wolfgang J. Runggaldier, 2023. "On the Separation of Estimation and Control in Risk-Sensitive Investment Problems under Incomplete Observation," Papers 2304.08910, arXiv.org, revised Nov 2023.
    17. Abdelali Gabih & Hakam Kondakji & Ralf Wunderlich, 2023. "Power Utility Maximization with Expert Opinions at Fixed Arrival Times in a Market with Hidden Gaussian Drift," Papers 2301.06847, arXiv.org, revised Jun 2024.
    18. Lleo, Sébastien & Runggaldier, Wolfgang J., 2024. "On the separation of estimation and control in risk-sensitive investment problems under incomplete observation," European Journal of Operational Research, Elsevier, vol. 316(1), pages 200-214.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jörn Sass & Dorothee Westphal & Ralf Wunderlich, 2017. "Expert Opinions And Logarithmic Utility Maximization For Multivariate Stock Returns With Gaussian Drift," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 1-41, June.
    2. Jorn Sass & Dorothee Westphal & Ralf Wunderlich, 2016. "Expert Opinions and Logarithmic Utility Maximization for Multivariate Stock Returns with Gaussian Drift," Papers 1601.08155, arXiv.org, revised Mar 2016.
    3. Christoph Knochenhauer & Alexander Merkel & Yufei Zhang, 2024. "Optimal Investment with Costly Expert Opinions," Papers 2409.11569, arXiv.org.
    4. Abdelali Gabih & Hakam Kondakji & Ralf Wunderlich, 2018. "Asymptotic Filter Behavior for High-Frequency Expert Opinions in a Market with Gaussian Drift," Papers 1812.03453, arXiv.org, revised Mar 2020.
    5. Abdelali Gabih & Hakam Kondakji & Ralf Wunderlich, 2022. "Well Posedness of Utility Maximization Problems Under Partial Information in a Market with Gaussian Drift," Papers 2205.08614, arXiv.org, revised Jul 2024.
    6. Abdelali Gabih & Hakam Kondakji & Ralf Wunderlich, 2023. "Power Utility Maximization with Expert Opinions at Fixed Arrival Times in a Market with Hidden Gaussian Drift," Papers 2301.06847, arXiv.org, revised Jun 2024.
    7. Abdelali Gabih & Hakam Kondakji & Ralf Wunderlich, 2024. "Power utility maximization with expert opinions at fixed arrival times in a market with hidden Gaussian drift," Annals of Operations Research, Springer, vol. 341(2), pages 897-936, October.
    8. Kristoffer Lindensjö, 2016. "Optimal investment and consumption under partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 87-107, February.
    9. Kristoffer Lindensjö, 2016. "Optimal investment and consumption under partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 87-107, February.
    10. Abdelali Gabih & Ralf Wunderlich, 2023. "Portfolio Optimization in a Market with Hidden Gaussian Drift and Randomly Arriving Expert Opinions: Modeling and Theoretical Results," Papers 2308.02049, arXiv.org, revised Jun 2024.
    11. Kexin Chen & Hoi Ying Wong, 2022. "Duality in optimal consumption--investment problems with alternative data," Papers 2210.08422, arXiv.org, revised Jul 2023.
    12. Kexin Chen & Hoi Ying Wong, 2024. "Duality in optimal consumption–investment problems with alternative data," Finance and Stochastics, Springer, vol. 28(3), pages 709-758, July.
    13. Katia Colaneri & Stefano Herzel & Marco Nicolosi, 2021. "The value of knowing the market price of risk," Annals of Operations Research, Springer, vol. 299(1), pages 101-131, April.
    14. 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.
    15. 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.
    16. Michele Longo & Alessandra Mainini, 2015. "Learning and Portfolio Decisions for HARA Investors," Papers 1502.02968, arXiv.org.
    17. Zongxia Liang & Qi Ye, 2024. "Optimal information acquisition for eliminating estimation risk," Papers 2405.09339, arXiv.org.
    18. Anton A. Shardin & Michaela Szölgyenyi, 2016. "Optimal Control Of An Energy Storage Facility Under A Changing Economic Environment And Partial Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-27, June.
    19. Rudiger Frey & Abdelali Gabih & Ralf Wunderlich, 2013. "Portfolio Optimization under Partial Information with Expert Opinions: a Dynamic Programming Approach," Papers 1303.2513, arXiv.org, revised Feb 2014.
    20. Wolfgang Putschögl & Jörn Sass, 2008. "Optimal consumption and investment under partial information," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 31(2), pages 137-170, November.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1402.6313. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.