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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
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    File URL: http://arxiv.org/pdf/1402.6313
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    References listed on IDEAS

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    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. 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.
    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.
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    Cited by:

    1. 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.
    2. repec:wsi:ijtafx:v:20:y:2017:i:04:n:s0219024917500224 is not listed on IDEAS
    3. 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.

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