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Portfolio Optimization under Partial Information with Expert Opinions: a Dynamic Programming Approach

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  • Rudiger Frey
  • Abdelali Gabih
  • Ralf Wunderlich

Abstract

This paper investigates optimal portfolio strategies in a market where the drift is driven by an unobserved Markov chain. Information on the state of this chain is obtained from stock prices and expert opinions in the form of signals at random discrete time points. As in Frey et al. (2012), Int. J. Theor. Appl. Finance, 15, No. 1, we use stochastic filtering to transform the original problem into an optimization problem under full information where the state variable is the filter for the Markov chain. The dynamic programming equation for this problem is studied with viscosity-solution techniques and with regularization arguments.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1303.2513
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    References listed on IDEAS

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    1. 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.
    2. 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..
    3. Mark H. A. Davis & Sebastien Lleo, 2009. "Jump-Diffusion Risk-Sensitive Asset Management," Papers 0905.4740, arXiv.org, revised Mar 2010.
    4. Jörn Sass & Ralf Wunderlich, 2010. "Optimal portfolio policies under bounded expected loss and partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(1), pages 25-61, August.
    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. 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.
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    Citations

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    Cited by:

    1. Anton A. Shardin & Michaela Szolgyenyi, 2016. "Optimal Control of an Energy Storage Facility Under a Changing Economic Environment and Partial Information," Papers 1602.04662, arXiv.org, revised Apr 2016.
    2. Michaela Szolgyenyi, 2016. "Dividend maximization in a hidden Markov switching model," Papers 1602.04656, arXiv.org.
    3. Szölgyenyi Michaela, 2015. "Dividend maximization in a hidden Markov switching model," Statistics & Risk Modeling, De Gruyter, vol. 32(3-4), pages 143-158, December.
    4. 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 Feb 2024.
    5. 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.
    6. 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.
    7. 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.
    8. Davis, Mark & Lleo, Sébastien, 2020. "Debiased expert forecasts in continuous-time asset allocation," Journal of Banking & Finance, Elsevier, vol. 113(C).
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.

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