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Optimizing the terminal wealth under partial information: The drift process as a continuous time Markov chain


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  • Jörn Sass


  • Ulrich Haussmann


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    We consider a multi-stock market model where prices satisfy a stochastic differential equation with instantaneous rates of return modeled as a continuous time Markov chain with finitely many states. Partial observation means that only the prices are observable. For the investor’s objective of maximizing the expected utility of the terminal wealth we derive an explicit representation of the optimal trading strategy in terms of the unnormalized filter of the drift process, using HMM filtering results and Malliavin calculus. The optimal strategy can be determined numerically and parameters can be estimated using the EM algorithm. The results are applied to historical prices. Copyright Springer-Verlag Berlin/Heidelberg 2004

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 8 (2004)
    Issue (Month): 4 (November)
    Pages: 553-577

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    Handle: RePEc:spr:finsto:v:8:y:2004:i:4:p:553-577

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    Keywords: Portfolio optimization; partial information; continuous time Markov chain; HMM filtering; stochastic interest rates;


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    Cited by:
    1. Abdelali Gabih & Hakam Kondakji & J\"orn Sass & Ralf Wunderlich, 2014. "Expert Opinions and Logarithmic Utility Maximization in a Market with Gaussian Drift," Papers 1402.6313,
    2. Eckhard Platen & Wolfgang Runggaldier, 2007. "A Benchmark Approach to Portfolio Optimization under Partial Information," Asia-Pacific Financial Markets, Springer, vol. 14(1), pages 25-43, March.
    3. Özge Alp & Ralf Korn, 2011. "Continuous-time mean-variance portfolio optimization in a jump-diffusion market," Decisions in Economics and Finance, Springer, vol. 34(1), pages 21-40, May.
    4. Thomas Lim & Marie-Claire Quenez, 2010. "Portfolio optimization in a default model under full/partial information," Papers 1003.6002,, revised Nov 2013.
    5. Elliott, Robert J. & Siu, Tak Kuen & Badescu, Alex, 2010. "On mean-variance portfolio selection under a hidden Markovian regime-switching model," Economic Modelling, Elsevier, vol. 27(3), pages 678-686, May.
    6. Markus Hahn & Sylvia Frühwirth-Schnatter & Jörn Sass, 2009. "Estimating models based on Markov jump processes given fragmented observation series," AStA Advances in Statistical Analysis, Springer, vol. 93(4), pages 403-425, December.
    7. Tomas Björk & Mark Davis & Camilla Landén, 2010. "Optimal investment under partial information," Computational Statistics, Springer, vol. 71(2), pages 371-399, April.
    8. Wolfgang Putschögl & Jörn Sass, 2008. "Optimal consumption and investment under partial information," Decisions in Economics and Finance, Springer, vol. 31(2), pages 137-170, November.
    9. R\"udiger Frey & Abdelali Gabih & Ralf Wunderlich, 2013. "Portfolio Optimization under Partial Information with Expert Opinions: a Dynamic Programming Approach," Papers 1303.2513,, revised Feb 2014.
    10. Björk, Tomas & Davis, Mark H.A. & Landén, Camilla, 2010. "Optimal Investment under Partial Information," Working Paper Series in Economics and Finance 739, Stockholm School of Economics.
    11. Liang, Zhibin & Bayraktar, Erhan, 2014. "Optimal reinsurance and investment with unobservable claim size and intensity," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 156-166.
    12. Jörn Sass & Ralf Wunderlich, 2010. "Optimal portfolio policies under bounded expected loss and partial information," Computational Statistics, Springer, vol. 72(1), pages 25-61, August.
    13. Agostino Capponi & Jose Enrique Figueroa Lopez & Andrea Pascucci, 2013. "Dynamic Credit Investment in Partially Observed Markets," Papers 1303.2950,, revised Jun 2014.
    14. Watanabe, Yûsuke, 2013. "Asymptotic analysis for a downside risk minimization problem under partial information," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 1046-1082.


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