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Optimal Investment under Partial Information

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Author Info

  • Björk, Tomas

    ()
    (Dept. of Economic Statistics, Stockholm School of Economics)

  • Davis, Mark H.A.

    ()
    (Imperial College, London)

  • Landén, Camilla

    ()
    (KTH)

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    Abstract

    We consider the problem of maximizing terminal utility in a model where asset prices are driven by Wiener processes, but where the various rates of returns are allowed to be arbitrary semimartingales. The only information available to the investor is the one generated by the asset prices and, in particular, the return processes cannot be observed directly. This leads to an optimal control problem under partial information and for the cases of power, log, and exponential utility we manage to provide a surprisingly explicit representation of the optimal terminal wealth as well as of the optimal portfolio strategy. This is done without any assumptions about the dynamical structure of the return processes. We also show how various explicit results in the existing literature are derived as special cases of the general theory.

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    File URL: http://swopec.hhs.se/hastef/papers/hastef0739.pdf
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    Bibliographic Info

    Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 739.

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    Length: 30 pages
    Date of creation: 26 Feb 2010
    Date of revision:
    Handle: RePEc:hhs:hastef:0739

    Note: Published in: Mathematical Methods in Operations Research (2010),Volume 71, Number 2, pp 371-399
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    Related research

    Keywords: Optimal control; investment theory; filtering;

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    References

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    1. Dothan, Michael U & Feldman, David, 1986. " Equilibrium Interest Rates and Multiperiod Bonds in a Partially Observable Economy," Journal of Finance, American Finance Association, vol. 41(2), pages 369-82, June.
    2. Gennotte, Gerard, 1986. " Optimal Portfolio Choice under Incomplete Information," Journal of Finance, American Finance Association, vol. 41(3), pages 733-46, July.
    3. Feldman, David, 1992. "Logarithmic Preferences, Myopic Decisions, and Incomplete Information," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(04), pages 619-629, December.
    4. Brennan, Michael J & Xia, Yihong, 2001. "Assessing Asset Pricing Anomalies," Review of Financial Studies, Society for Financial Studies, vol. 14(4), pages 905-42.
    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.
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    Cited by:
    1. Branger, Nicole & Kraft, Holger & Meinerding, Christoph, 2014. "Partial information about contagion risk, self-exciting processes and portfolio optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 18-36.
    2. Xiang Yu, 2011. "An Explicit Example Of Optimal Portfolio-Consumption Choices With Habit Formation And Partial Observations," Papers 1112.2939, arXiv.org, revised Aug 2012.
    3. Claudio Fontana & Bernt {\O}ksendal & Agn\`es Sulem, 2013. "Market viability and martingale measures under partial information," Papers 1302.4254, arXiv.org, revised Oct 2013.

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